Talk:Introduction to entropy/Archive 1

The first paragraph
--- Feel free to revise the following!! I think the present (9 am PST, 26 October is good, but too dense, too many ideas per paragraph.) Maybe this is a useful small-stete wise start: (FLL) --- -- I would like to draw attention to a first paragraph example for this article, note no math, at User:CoffeHousePhilosopher/sandbox Please pick it apart at your convenience, then we can rewrite it since it does indeed appear elsewhere...CoffeHousePhilosopher (talk) 07:50, 31 October 2017 (UTC) Ron the Coffee House Philosopher

The concept of entropy is central to the second law of thermodynamics. A modern version of the second law is "Energy of all types spontaneously changes from being localized to becoming more dispersed or spread out, if it is not hindered". A simple example would be a hotter bar of iron touching a cooler bar. Always the energy of the hotter spreads out to the cooler until both are at the same temperature. Then, entropy (or better, entropy change, &Delta;S) is the quantitative measure of how much energy, q, has been dispersed in a process, divided by the temperature, T, at which it occurs. This yields the fundamental equation for entropy: q(reversible)/T.

(That "reversible" means that the process should be carried out at a temperature where each bar is almost the same -- the hotter only slightly warmer than the cooler so the energy would flow in reverse if there were only a slight change in the relative temperatures. When the temperature of one bar is considerably hotter than the other, as is most often the practical case, we can use calculus to 'paper-correct' the temperature difference. Our calculations simulate a series of reversible steps by treating the entropy change as though it occurred in tiny jumps or increments of temperature.)

There are two principal types of process involving energy change for which entropy measurement is especially valuable: heating (i.e., the transfer (spreading out) of energy from hotter to cooler and raising the temperature of 'the cooler'), or allowing the internal energy of a substance to become more spread out by allowing it to have more volume -- as in letting a gas expand or in mixing fluids (gases or liquids). Chemical reactions involve both types due to the release of energy (i.e., its dispersal to the surroundings) when new stronger bonds are formed as old ones are cleaved. (Endothermic reactions are the opposite: energy flows from the surroundings to become more dispersed in a system because that energy, in breaking bonds in the system, yield more particles that can more widely spread out that energy.)

The entropy of any substance at a given temperature, T, is given in tables of standard entropy as so many joules (energy)/T298 K. Actually, that final q/T 298 K is a sum and thus a &Delta;S of very many individiual measurements or calculations of q/T over very small &Delta;T changes from 0 K to T. Thus, the number for the entropy in joules/K is not the total amount of joules of internal energy in the substance (because the many increments of energy have each been divided by their T values). However, the standard entropy, listed in Tables at 298 K, is a useful rough comparison of the internal energy of every substance. EXAMPLE?? Graphite vs. diamond??  That is significant because it means a non-exact but qualitatively useful comparative value for the energy which a substance must have to exist at 298 K.  (The phrase in italics is the qualitative meaning of "energy that is unable to do work" or "energy that is unavailable for thermodynamic work". Of course, the internal energy of a substance A can be transferred to another that is colder, but then substance A can no longer exist at its initial temperature because its entropy has also decreased.) [Posted 26 Oct; revised 28 Oct FrankLambert 03:41, 28 October 2006 (UTC) ]

Entropy as measure of loss of heat or energy
Only just found this. As as asked on Talk:Entropy, where on earth do you get the idea that entropy is a measure of energy? They have different dimensions. It is like saying apples are a measure of oranges. It is completely unclear. However a worthy start. I'll try to look at it but I am very busy and my WP time has been diverted to something else. --Bduke 02:27, 28 October 2006 (UTC)
 * To clarify. The question here is addressed to Kenosis as the main author of the article, not to Frank. --Bduke 04:13, 28 October 2006 (UTC)
 * Dave_souza added that passage, so the question might reasonably be deferred to Dave. And I don't necessarily disagree with the passage adequately to jump in and change it, because the technical usage of the word "entropy" depends on how you're using it, given that virtually every field that uses the term seems to have their historical and current perspectives.  But... from a purely technical standpoint involving reasonable operational definitions in thermodynamics, this passage is a very reasonable expression of the concept.  It is widely accepted that a small Delta-S in a larger environment (where the entropy being described does not appreciably change the denominator reflecting the temperature of that environment) involves entropy expressed solely by the numerator.  And even where the denominator changes significantly (such as, for instance, where an engine heats up or cools down) we are still talking about a measure of energy in the process of being dispersed to, or from, or within, a place, structure, set of molecules, part, sector, or other definable place or region. ... Kenosis 04:29, 28 October 2006 (UTC)


 * I am very sorry -- I started this Talk:Introduction page and thought I had signed it. Thus Bduke I think! was properly questioning me. I was finishing the following and about to post it when a 'conflict' notice appeared. Here is my response to Bduke:


 * Bduke is certainly correct that entropy and energy have different dimensions. But the standard entropy of a substance is the result of q(energy) being dispersed to a substance (reversibly) divided by temperature at a theoretically 'infinite' number of (i.e, many) temperatures from 0 K to 298 K. Thus, energy input is explicitly involved in the standard entropy values of substance A and a substance O.


 * This is not at all like the impossibility of truly comparing apples to oranges -- it is roughly comparing an important ingredient in both, e.g., the amount of carbohydrate in Apples (~15%) to Oranges (~10%). I have long urged this as an important interpretation of what is in all elementary chemistry books, but never interpreted in approximate terms of energy required for the substance to exist at 298 K:. relatively obvious: that liquids have higher entropies than the corresponding solids, polyatomic gases more than monatomic, etc. -- but WHY can be answered now, if one considers the approximate energy needed for each to exist (as shown by their standard entropy values): polyatomic gases need more energy for their rotation, liquids must have enthalpy of fusion going from 0 K to 298 K, etc.,etc.  A remarkable article, strongly supporting my view by going quantitatively beyond it, has just appeared in the November JChemEducation that would satisy Bduke because the author uses the physicist's dimensionless 'sigma entropy'(S/l B to compare a large number of elements and compounds for their ln W, energy level occupancy -- a neat quant. idea. So don't chop my simple but important qualitative view! JChemEduc, 2006, 83, 1686-1694.  FrankLambert 05:04, 28 October 2006 (UTC)

OK, we seem to be clear about who the question is for! I do not disagree with the above. I disagree with the language. "Entropy is a measure of energy" suggests that they have the same dimension. This will confuse people. It is the word "measure" that is the problem. I'll look at the Nov JChemEd when it comes but that will not be for a while. --Bduke 06:13, 28 October 2006 (UTC)
 * Apologies for the inadequacies of my phrasing: I've added a reference to temperature which I think is the other main ingredient: perhaps it would be better to say "contributes to a measure of"? .. dave souza, talk 10:21, 28 October 2006 (UTC)

This is wrong: ".....even being motionless for an instant if two molecules with exactly the same speed collide head-on, ". Shock does not stop the motion. For exemple, 2 balls with opposed speed will depart with the same speed on the opposed direction according to Newton. Gtxfrance (talk) 01:29, 27 February 2009 (UTC)

The article is seriously confused by the inference of more than one definition of entropy. Further confusing absolute entropy with entropy change and the incorrect assumption that the calculation of one is capable of a complete accounting of the other is just plain wrong.. Gyroman (talk) 23:38, 15 September 2014 (UTC)

Aims of the article
As was discussed on Talk:Entropy, the aim here is to give an introduction suited to beginners: I've added a "Heat and entropy" section adapted from FrankLambert's work with the intention of making it more concise and giving it a more encyclopaedic tone: a section on Statistical thermodynamics should follow. I've tried to improve the intro a bit and made it shorter by moving content into "Origins and other uses" – the order of sections could be reviewed – but haven't yet tackled the important point Frank makes in above: in my opinion it's worth trying to move from a more traditional approach to the energy dispersal concept, but agree that a simpler start will be better for beginners. .. dave souza, talk 10:34, 28 October 2006 (UTC)


 * In my view, the aim of this entry is a very worthy one. Case in point: It is fascinating to see how in the past 30+ years, the Second Law has come to play a fundamental role in cutting edge discussions of cosmology, the astrophysics of black holes, the Anthropic principles, digital physics, and the arrow of time. Just look at Frank Tipler's respectful mentions of the Beckenstein bound. If there is one thing we know about the universe, it is that its entropy increases over time.


 * That said, the entry does not achieve that worthy aim very well for two reasons: (i) it is too technical (the level to aim at is that of Goldstein and Goldstein 1993), and (ii) it is totally beholden to the energy dispersal point of view. This entry should be written in a way that recognizes that nearly everything written about entropy during the last century defined it in a different way. That way may have been wrong, but it still needs to be explicated. I have no difficulty with this entry explaining entropy in two contradictory ways, with due warning given to the reader. That something as basic as entropy has become the subject of a vigorous debate over the past 20 odd years is not something to hide from the layity, but as a reason to celebrate the intellectual honesty of basic science.


 * Frank Lambert's website convinces me that over the course of this decade, energy dispersal has emerged as the new consensus in freshman chemistry texts. He has not convinced me that that consensus extends to contemporary specialist texts in physical chemistry and thermodynamics. As long as nearly all such specialist texts treat entropy in the traditional way, as a scalar measure of disorder among microstates, an entry such as this one will have to discuss the traditional definition politely.123.255.30.219 (talk) 18:17, 30 December 2008 (UTC)

Simple English Wikipedia?
I think this article would be more appropriate for the Simple English Wikipedia. If no one objects, I'm going to transwiki this and add the interwiki link. Axem Titanium 21:43, 16 January 2007 (UTC)
 * I object. Only do this if you can meet two criteria - (1) make entropy a lot clearer and have at least an introduction, and then individual introductions to each section that has a main article, that are sufficently clear for a reasonably prepared student to understand; and (2) write the introductory article in simple english. It too is far too complex in parts, and its language certainly does not meet the criteria for the simple english wikipedia. Note that this article was written because editors on entropy could not agree on the need to simplify that article or at least on how to simplify it. My personal view has always been that introduction to entropy should not exist and that entropy should give a sufficient introduction, but it does not do so. The simple english wikipedia does need an article on entropy but this in'nt it. Please try to work on entropy to make that better. --Bduke 22:21, 16 January 2007 (UTC)
 * This should in the simple English wiki?! I can't even understand it as it is. Please make the introduction simpler. Think of it like this; I am a random person who has heard the word "entropy" in an conversation. Now I want to look it up and find out what it means. Reading "a measure of certain aspects of energy in relation to absolute temperature. In thermodynamics, entropy is one of the three basic thermodynamic potentials: U (internal energy), S (entropy) and A (Helmholtz energy). Entropy is a measure of the uniformity of the distribution of energy." Isn't going to make a d*mn bit of sense to me. Please try to word the entry so that someone who doesn't understand physics at all, or at least only the very basics of physics--like high school physics, or even better, middle schoolphysics--can understand it. If that isn't possible, try to make a clearer path of the necessary research that needs to be done to understand it. Right now the introduction doesn't even give me an idea of where to begin. —Preceding unsigned comment added by Sailor Titan (talk • contribs) 01:02, 11 May 2009 (UTC)
 * BTW, a friend found a good link that gives an example of a simple explanation. Is it oversimplified? Probably. But it gives an idea, and starting with a complex explanation will leave the learner mystified.--Sailor Titan (talk) 01:17, 11 May 2009 (UTC)

Correct?
Is this line OK: "In calculations, entropy is symbolised by S and is a measure at a particular instant, a state function" 124.30.235.62 (talk) 08:02, 15 September 2008 (UTC)


 * Entropy is indeed symbolized by S and is a scalar measure as of a particular instant. Whether it is a state function in the sense of thermodynamics, I invite others to answer.123.255.30.219 (talk) 18:49, 30 December 2008 (UTC)

First, a concern on correctness: "Statistical mechanical entropy is mathematically similar to Shannon entropy which is part of information theory, where energy is not involved." Second, see the corresponding addendum to the subsequent Brillouin section. —Preceding unsigned comment added by Rwestafer (talk • contribs) 18:41, 17 August 2009 (UTC)

Entropy, information, and Brillouin
I gather that more and more of you out there share the view that entropy in physics and entropy in information theory are like two ships passing in the night; neither has relevance for the other. I am very reluctant to agree, because of my respect for the following title and its author:

Léon Brillouin, 1964. Scientific Uncertainty and Information. Academic Press.

123.255.30.219 (talk) 18:49, 30 December 2008 (UTC)

Another related concern by a separate reader: especially about this statement, "Statistical mechanical entropy is mathematically similar to Shannon entropy which is part of information theory, where energy is not involved." Alright, how would one transmit information without energy, or maintain a physical state (obviously the state embodies some information: spin, etc.) without acknowledging some energy? With quantum computing around the corner, I think we must be careful here. I challenge the contributors to distinguish between bits and "up"/"down" electron spin states. The units need not be Joules for the quantity to represent energy (furthermore, if we're talking about rest mass or energy, the units could be kg). Information theory just generalizes these specific physical quantities. —Preceding unsigned comment added by Rwestafer (talk • contribs) 18:47, 17 August 2009 (UTC)
 * Entropy (information theory) is measure of the uncertainty associated with a random variable, not a measure of the energy used to send that variable. . dave souza, talk 20:07, 17 August 2009 (UTC)
 * Dave, would you say the variance of a normally distributed random variable corresponds to its power? (n.b. - not talking about statistical power)  Others agree with this viewpoint: "Since the variance of a Gaussian process is equivalent to its power, it is conventional to call this variance the noise power." (See Shannon–Hartley theorem)  So some "energy," then, is the area under the curve, where the center-of-energy is the mean.  The term energy is not alien to information theory.  Do you prefer its removal?  --Ryan Westafer (talk) 02:23, 19 August 2009 (UTC)
 * Right, so looking at that the issue is that energy is only involved to the extent that it affects information transmission. . . dave souza, talk 10:43, 19 August 2009 (UTC)
 * I'll argue it's intrinsically involved. Maybe you would agree that symbols, bits or arrangements of multiple bits, constitute the information to be transmitted?  Whether a symbol is drawn in the sand or "written" into the electrical potential along a wire, the information corresponds to a rearrangement of matter or energy - which typically corresponds to some potential or stored energy.  The sand will settle and an electrical pulse will dissipate (we should admit the very physical Second Law of Thermodynamics in discussing entropy).  Noise "hides" information (localized energy) by homogenizing ... like rain on the sand or incoming radio waves on a wire.  I originally wrote "erases" information, but really, with significant work (exertion of energy), one can ascertain the original signal from inspection of the dissipation process, e.g. how the sand grains fell.  This is analogous to how clever coding schemes can transmit signals in the presence of significant noise - more work (literally/physically) is required by a computer to decode the message, but it survives the noisy channel.  The signal-to-noise ratio used in the Shannon–Hartley theorem is a ratio of signal and noise powers which, along with bound of the domain (bandwidth), determines the capacity of a channel to carry symbols (which I just argued have a quantifiable energy to be dissipated).  Does this help show the relations among entropy, dissipation, energy, information, and noise?  —Preceding unsigned comment added by Rwestafer (talk • contribs) 13:47, 19 August 2009 (UTC)

Entropy - what IS it?
What IS entropy? I want to have a simple definition: Entropy is "blah and blah". I do not care about what it is "central" to, or what it is "related" to. "Entropy is a thermodynamic quantity" is a good start - but it says nothing as to what it MEANS.

For example I can say that "kilogram" is a "one of the SI units", but it really MEANS nothing until I say that it is the "base unit of mass".

Now I don't know what "Entropy" is so I can't add or modify the definition, but can merely point out my confusion.

I am always amazed by the lack of actual definition of things in books, journals and in particular Wikipedia. Drozdyuk (talk) 18:37, 14 July 2010 (UTC)


 * I have attempted to clarify and update the definition to: "Entropy is a quantifiable measure of how evenly the heat is distributed in the system. Every time heat flows from a hot spot to a cold spot, entropy increases, as heat becomes more distributed throughout the system. Every time heat flows from a cold spot to a hot spot, entropy decreases, as heat becomes more concentrated in certain part of the system." Drozdyuk (talk) 18:36, 14 July 2010 (UTC)


 * I think your new definition is a good one. (On the matter of entropy I am a thermodynamicist and think of entropy in terms of heat, and the flow of heat.  Others are informationists and think of entropy in terms of information.  They might be inclined to reject your definition.)


 * You could further improve your edit by citing the source of your definition to enable independent verification. At WP:Verifiability it says The threshhold for inclusion in Wikipedia is verifiability, not truth.  Dolphin  ( t ) 22:51, 14 July 2010 (UTC)


 * OK. I've added a reference to the end of the paragraph. --Drozdyuk (talk) 12:34, 15 July 2010 (UTC)

The person who pointed out the confusion is totally correct. Everyone who has provided explanations has made explanations that are true and which they understand but which actually are not explanations at all. If you didn't know what entropy was before reading this article you certainly won't afterwards and the notion that it is a non technical explanation is laughable - the very first thing it does is goes into a delta equation!!

I would explain it something like this: Thermodynamic Entropy: Energy unavailable for work; ... [don't bother - unsigned and your confused, remember, see below]  ... Thus by doing work and using energy, you make some energy unavailable for further work, thereby increasing Entropy. —Preceding unsigned comment added by 88.104.102.84 (talk) 07:59, 4 November 2010 (UTC)


 * Your not alone.. the State of Confusion is quite general. The definition of the term entropy is confused because of how Rudolf Clausius, (who coined it), actually discovered it. What he observed was the results of the second law operating on a system involving heat and work transfer. His equation for entropy describes only the change in this state variable during such a process. He did not define entropy at its most fundamental level.


 * Fundamentally entropy has nothing to do with heat or work or energy of any kind!


 * It was Ludwig Boltzmann who discovered the meaning of entropy. It is his equation (inscribed by Max Planc on his gravestone) s = k.ln W which defines it, (should be tattooed on every thermo lecturers forehead). The Boltzman constant 'k' was required to give entropy its units (joule/deg) because the only variable in it 'W', is just a number W = (1/probability that state should exist). In other words entropy and the driving principle of the second law is completely defined in terms of probability. The dissipation of energy in all its forms is only a result of the second law not the driver of it. Hence the definition..

Entropy: is a quantitative measure of disorder [Cambridge Encyclopedia]


 * Since the Clausius equation is easily derived from the Boltzmann equation by making just one simplifying assumption, the only state possible is the most probable (W max)[Wark], (never far from the truth for real thermodynamic systems with eons of atoms) the simplest statement of the second law is..
 * Left to itself any system of particles will tend toward its most probable state. Vh mby (talk) 01:52, 23 May 2014 (UTC) user name changed to Gyroman (talk) 10:02, 8 April 2015 (UTC)

This thread has been perhaps the most useful read for my understanding of entropy, even after a year of engineering at a good university. Thanks guys :) — Preceding unsigned comment added by 74.116.207.71 (talk) 23:15, 10 July 2014 (UTC)
 * Thank you (so why is this not clear in the article?) Gyroman (talk) 10:02, 8 April 2015 (UTC)


 * WP began as a noble and worthy project. Sadly, over time it has primarily become a place for would-be academicians to bloviate -  seemingly without constraint.  More and more, these "scientific"-type articles devolve from fairly easily understood topics, into a jumble of incomprehensible jargon that the casual reader has no chance whatsoever at understanding.  For that matter, most of the technical articles are so full of obscure technical terms, and are so poorly written, that even an educated expert in the field is left shaking his/her head.  I am saddened to look on as this site becomes so useless to me and my youngsters that I no longer direct them here for any meaningful information in the sciences.  Hopefully, the ego inflation of the collective "authors" was worth the deprecation in value, and ultimately, the demise of this site.  But please, carry on blathering about the Clausius and Boltzmann equations.  We shall all sit by silently as you dazzle us with your expertise... and we learn nothing.  — Preceding unsigned comment added by 98.194.39.86 (talk) 11:13, 30 October 2016 (UTC)

Reference?
As a suggestion, I don't think that "the science against evolution" website is the best source. Olin (talk) 16:31, 25 July 2010 (UTC)

Totally agree. Who snuck that in there? It seems a truly bizarre choice for an authoritative reference for a basic comment about entropy. Hardly NPOV! 86.162.59.150 (talk) 17:27, 14 November 2010 (UTC)

Fixed an error
Changed from ("Heat and entropy" section):


 * "...repeatedly colliding and therefore exchanging energy so that their individual speeds are always changing, even being motionless for an instant if two molecules with exactly the same speed collide head-on, before another molecule hits them and they race off, as fast as 2500 miles an hour. (At higher temperatures average speeds increase and motional energy becomes proportionately greater.)"

To just:


 * "...repeatedly colliding and therefore exchanging energy so that their individual speeds are always changing. Assuming an ideal gas model, average kinetic energy increases linearly with temperature, so the average speed increases as a square root of temperature."

The bold part in the given excerpt was wrong. In a minimalistic model such as the ideal gas, kinetic energy is the only component contributing to the total energy of the system. It follows, that the kinetic energy of the system is conserved. Interactions between molecules are treated as perfectly elastic collisions - kinetic energy and momentum are both conserved. The situation, where two molecules with non-zero combined kinetic energy before the interaction have no kinetic energy after it, is therefore an impossibillity.

The molecules would be moving away from each other with the same speeds after the interaction in this specific case - conservation of KE and momentum are easily imaginable.

sprayer_faust 12:25, 8 February 2012 (UTC) — Preceding unsigned comment added by Sprayer faust (talk • contribs)

This page should be merged with Entropy.
This page should be merged with entropy or sent to the Simple English Wikipedia. I understand both to be objectionable ideas, the latter especially but a decision has to be made regarding this. -Anon 8/10/12 4:58 Indian Standard Time — Preceding unsigned comment added by 49.249.142.61 (talk) 11:29, 10 August 2012 (UTC)
 * Why does "a decision have to be made regarding this"? Dolphin  ( t ) 11:44, 11 August 2012 (UTC)

There is no reason why a decision has to be made or indeed why it should be merged or sent to the Simple English Wikipedia. First, the Simple English Wikipedia uses a limited set of words defined for Simple English. It is not the same as writing an introduction. Second, there are lots of "Introduction to .." articles and they are a good idea. The entropy article is far too complex for readers coming to the concept for the first time. Even the introduction to entropy article is somewhat daunting. -- Bduke   (Discussion)  23:53, 11 August 2012 (UTC)
 * I have to agree with that last sentence. I believe the main article could be simpler and more direct than this introduction, which tends to waffle.  See my comments below on Chris Bishop's video.
 * What's needed is an article whose entropy is sufficiently low as to make it relatively easy to distinguish the edits that raise its entropy from those reducing it. This doesn't seem to be the case right now for either article, witness the increase in entropy of the main article over the past couple of days.  Vaughan Pratt (talk) 18:27, 10 November 2014 (UTC)

Appreciation for this page
I would simply like to thank the people who put their time and effort into creating and developing this page, and to those in the discussion above who stood up for its value and importance. Tonight I really, really wanted to get a basic grasp of the term, but couldn't understand most of the main article. I followed the link to this introduction, and found that I could follow most of it. I'm not stupid, but the conservatory of music that I attended just didn't have a very strong physics department. DSatz (talk) 02:01, 27 October 2012 (UTC)

Ditto that. I also could not make much sense of the introductory text of the more "technical" entropy article. Then, I followed the link to this article and found its explanation of entropy far more useful.

I object to the proposals to move this article to the Simple English Wikipedia ("intended for people whose first language is not English"). This "Introduction to entropy" was not written with a smaller vocabulary; it's written more concisely. Some of the comments on this article's Talk page reflect a pretentious attitude that ambiguously defined technical jargon is a desired part of an encyclopedic article. I don't think that the ego of an unclear writer should be stroked by delegating this article to the "Simple Wikipedia" as if it is inferior to the other one. Ideogon (talk) 22:21, 4 January 2013 (UTC)

Simple Video explanation of Entropy
I found an excellent explanation of the concept of Entropy in a Royal Institute video but I am unsure of the policy regarding videos on Wikipedia, so I'll leave it here for someone with more experience than me to add if they feel it is a good idea. The relevant section in the video is from 48:22 to 51:07. http://www.youtube.com/v/ti_E2ZKZpC4&start=2902&end=3067 86.2.95.179 (talk) 10:28, 23 May 2013 (UTC)
 * Why stop there? At 51:07 Chris Bishop was just getting started.  The explanation up to that point could just as well have been for Entropy (information theory) (compare the probabilities of seeing a homogeneous bit string---all ones or all zeros---and one with a roughly equal number of 0's and 1's).  He then goes on to illustrate entropy in chemistry with the example of the temperature-regulated conversion of nitrogen dioxide into dinitrogen tetraoxide (by cooling, which lowered the entropy of the gas) and back (by heating, which raised its entropy).  Had time permitted he could have pointed out that the second law of thermodynamics was not violated in the former case because when the cold water cooled the gas, the entropy of the water increased by more than the decrease in entropy of the gas (and conversely when the hot water heated the gas the entropy of the gas increased by more than the decrease in entropy of the water).  Vaughan Pratt (talk) 17:23, 10 November 2014 (UTC)
 * Going back to the 48:22-51:07 portion of Bishop's video, understood in terms of bit strings, the distinction between physical state and thermodynamic state is loosely analogous to the distinction between a particular bit string and its Hamming weight or number of ones. If one takes ones and zeros to be very tiny, of weight respectively 1 and 0 micrograms, then a bit string of length a million that is either weightless (all bits zero) or weighs 1 g (all ones) has very low probability and therefore very low entropy, while one that weighs 0.5 g has much higher probability and therefore higher entropy.  This is still true even if the weight is only known to within a milligram.  Determination of the "thermodynamic state" thus understood is easy: just weigh the string to within the available precision.  To know the physical state you have to learn the state of every individual bit, with no forgiveness for imprecision.  Vaughan Pratt (talk) 17:55, 10 November 2014 (UTC)

Explanation
In the Explanation section, it says:

I think the "Why?" could be answered by editing as follows:
 * Following the formalism of Clausius, the first definition can be mathematically stated as:
 * $${\rm d}S = \frac{{\rm \delta}q}{T}.$$
 * Where dS is the change in entropy, δq is the heat added to the system, which holds only during a reversible process, and T is temperature.

What do you think? JDHeinzmann (talk) 01:14, 12 March 2014 (UTC)
 * Where dS is the change in entropy, δq is the heat added to the system, which holds only during a reversible process (because an irreversible process would introduce more entropy), and T is temperature.

A macrostate is definitely NOT what we know about the system..! It is NOT defined by the macroscopic variables 'pressure, temperature, volume'.. My undergrad text on Thermodynamics 'Wark' will tell you that. Many different macrostates will give you the same macroscopic measures of those variables.. Macrostates are time snapshots of the precise distribution for every particle all the discrete attributes of their states which sum to give the overall state of the system. Attributes include all forms of energy but also includes spacial attributes like position and logical attributes like value with respect to an external reference. Which is one reason entropy is 'extrinsic'. Gyroman (talk) 23:34, 7 April 2015 (UTC)

Truly Awful
This is hardly at an 'introductory' level. Furthermore, despite its density it seems to actually betray a lack of understanding. Entropy is a measure of disorder. Disorder increases over time because for every change in state there are more pathways to disorder than there are to order. When non-trivial numbers are involved the probability of going significantly toward an ordered state is vanishingly small. It is physically possible for a tipped jar of a thousand coins to come up all heads. As a practical matter someone familiar with the math can comfortably guarantee that although technically possible it is never going to happen. DeepNorth (talk) 16:16, 7 November 2014 (UTC)
 * I second this objection, especially to the first paragraphs of the page. The metaphor / allegory of the film shown in reverse is extremely confusing and contributes little to a clear understanding of the concept of entropy. I am not an expert, but if some kind of consensus is needed to overhaul the introduction, here's my two cents. Iconofiler (talk) 20:02, 20 February 2015 (UTC)


 * I rather like the idea of the film in reverse. It shows things that do not happen because of the second law. However it needs putting in a different context. The very first sentence is not that context and indeed that is a really bad first sentence because it confuses the reader from the start. All the articles on entropy are not in good shape. This just illustrates what I have know since I started a career as a chemistry educator over 50 years ago. Teaching thermodynamics in general and entropy in particular is extremely difficult if the students do not have strong mathematics and you can then present it in a mathematical way. Many editors of these articles appear to be physics graduates who learnt entropy that way, but it can not be the way to write articles in an encyclopedia. I have to say that I still do not know how to do it, so I generally keep away from these articles except for watching them. This article could be a good place to start, but remember it is an introduction and it should not contain material that is not introductory that should be elsewhere. -- Bduke   (Discussion)  20:59, 20 February 2015 (UTC)


 * I heartily concur with the above.. this is not only a very poor introduction but quite misleading in several aspects. See my comment under 'Explanation' concerning macrostates and macro properties.. Gyroman (talk) 23:46, 7 April 2015 (UTC)


 * The title of this article is an *introduction* to entropy.


 * If this were an article on temperature, the target audience would not want to hear, in the introduction, about how temperature is proportional to the energy per degree of freedom in the limit of an infinite number of particles, with suitable modifications for applications in the quantum mechanical regime. They would want to know, first of all, is there an everyday experience that I can use to gain an intuitive understanding of temperature? Yes - hot and cold.


 * Likewise for entropy, the target audience is not someone who wants to hear about how entropy is the logarithm of the number of microstates, assuming equal apriori probability, that yield a given macrostate, ok? So tell me, what is an everyday experience that you can use to gain an intuitive understanding of entropy? It's become evident (Caratheodory, Lieb and Yngvason) that most fundamental property of entropy is practical irreversibility (or "adiabatic inacessibility") for "macroscopic" systems - the second law - and that is accessible to everyday experience. Without the property of irreversibility, entropy as a concept is useless. It follows that the introduction should be giving a feel for irreversibility in everyday life. Correct me if I am wrong, but this article is for people who do not want to solve a textbook problem, or get a warm fuzzy feeling by learning phrases that the wizards repeat, but rather people who want to gain a non-mathematical intuitive understanding of entropy, however much that is possible. The dorky examples of irreversibility at the beginning of the article actually strike at the core of the concept of entropy.


 * It's the people who think they understand entropy who complain about this article, when what they actually understand is how to pose and solve problems in a language designed to permit a solution. Like quantum mechanics, you don't need to understand what you are doing to just shut up and calculate. Or else it's people regurgitating phrases that they have not inspected and, upon inspection, have little meaning. This includes teachers who, understandably, want to give their students a feeling of understanding and accomplishment, but sometimes do so at the expense of reality. In reality, entropy is a very difficult concept to understand and there is no shame for an expert to admit they don't fully get it. As Von Neumann said "nobody really understands entropy".


 * With regard to catch phrases: "In a physical system, entropy provides a measure of the amount of thermal energy that cannot be used to do work" - warm and fuzzy. Entropy, among other things, can serve as a measure of the amount of thermal energy in a high-temperature reservoir that cannot be used to do work, when two heat reservoirs at different temperatures are used to extract that work. Oh, there goes my warm fuzzy feeling, lets just use the first statement.


 * And while we are at it, "entropy is a measure of disorder" is even worse. Its a phrase which is useless until "disorder" is defined, and once you tie that definition down, it amounts to ... wait for it ... "disorder is a monotonically increasing function of entropy". Oh, and "dispersal of energy". It turns out its not necessarily a dispersal in space, but is generally a dispersal in some parameter space which is designed to indicate a dispersal of energy as entropy increases. Real helpful. To be even more precise, entropy is not even the logarithm of the number of microstates that yield a given macrostate. Thermodynamics is a macroscopic theory, and entropy is defined macroscopically, in the real world, without any reference to unobservable particles and probabilities. Statistical mechanics and the atomic theory of matter provide an *explanation* of thermodynamic entropy, but not a definition, and anyone who confuses the two belongs in that category of "physics graduates who learnt entropy that way".


 * I am not saying this article is wonderful, it's not, but it does not need to be transformed into a bunch of mindless catch-phrases or nit-picked to the point that it serves to replace the main article on entropy. It needs to provide everyday experiences and thought experiments that provide a rudimentary, intuitive concept of entropy, minimizing the use of concepts that require some time to master. PAR (talk) 02:48, 8 April 2015 (UTC)


 * Many physicists, particularly the low-level ones without real research credentials, make their living from teaching, and there appears to be a cabal to make readily available explanations of entropy as dense and confusing to follow as possible so as to keep the demand for physics teachers artificially high. (I'm only partly joking.)--Anders Feder (talk) 21:47, 10 May 2015 (UTC)

I am a new Wikipedian
I am a new Wikipedian and decided that my first contribution was to alter the date of first 'cn' to October 2015 and convert the first what to link to Physical process article. Fill free to undo those changes. In regards to the first 'citation needed' I believe it should be removed because it requests citation of a statement of the type: "Everyone knows something" on an introductory article. All rules are valid as long they make sense and when they don't they don't apply.

Airliner 15:04, 28 October 2015 (UTC) — Preceding unsigned comment added by DomFerreira01 (talk • contribs)

I just added cnDiscuss because I feel [Citation needed] distracts the reader and unnecessary on the statement above. I suggest unless someone can provide the necessary citation in a period of time, the cn should be removed. Airliner 22:01, 4 November 2015 (UTC) — Preceding unsigned comment added by DomFerreira01 (talk • contribs) 22:03, 4 November 2015‎


 * This is not a statement that needs a citation. An explanation of the statement comes immediately after, and if any citation is needed, it is for that explanation. "if one watches a movie of everyday life running forward and in reverse, it is easy to distinguish between the two." Do we need a citation for something so obvious? If this statement needs a citation, then every sentence in the article needs a citation. PAR (talk) 13:54, 5 November 2015 (UTC)

Entropy as disorder
I removed the first sentence describing entropy as a measure of molecular disorder.


 * Entropy is macroscopic, it is defined in macroscopic terms, it is measured without reference to molecular disorder, or atomic theory, or statistical mechanics. Statistical mechanics, including the information approach to entropy is an EXPLANATION of entropy, it is not the definition. The disorder, or lack of information, cannot be measured without the attending explanation.


 * "Disorder" is generally a vague concept, but in the reference quoted it is defined as a "lack of information" which means it is related to the Shannon information entropy. Again, this is a microscopic explanation of entropy, not the definition and again, if you accept the connection between information entropy and thermodynamic entropy, it amounts to saying that disorder is entropy. Not helpful.


 * The reader needs to understand macroscopic entropy, at least roughly, before appreciating the microscopic explanation. Without it, the microscopic explanation has no operative meaning. This does not mean the microscopic theory does not provide huge insight into entropy. But without a macroscopic understanding, however rough, you are left with a huge insight into nothing.

The purpose of this article is to introduce entropy. The microscopic explanation of entropy belongs further down in the article, not in the first sentence. PAR (talk) 19:56, 11 October 2016 (UTC)


 * Technically you might be correct, but an understanding of the finer points requires a starting point and to begin with a definition that is commonly understood, and close enough, is the place to begin. If you want to be absolutely correct the introductory sentence would be unintelligable to all but the 0.1% of the people who come to read the article, which would be those who don't really need to read the article in the first place as they know the material. To say, "For a process to be viable, it must increase the disorder of the universe," is accurate enough. Once you have that starting point it might be possible to elaborate and say, "or some subset of the universe." The writers of these article should try to keep in mind for whom they are writing. If you already have a through understanding of a technical subject and write at the highest level possible, you are missing the point. The article should not be written for you unless you are here to satisfy your own vanity. Zedshort (talk) 20:25, 11 October 2016 (UTC)

Rewrite the introduction that has deteriorated
I have restored the original introduction with a lot of modifications. The introduction has deteriorated by introducing a bundle of useless catch-phrases which do little to nothing to bring the uninitiated to an introductory understanding of entropy.

Please, please, before reverting this, please try to understand my point. I am in total agreement with Zedshort when he writes "The writers of these article should try to keep in mind for whom they are writing. If you already have a through understanding of a technical subject and write at the highest level possible, you are missing the point. The article should not be written for you unless you are here to satisfy your own vanity." I would add that it should not be written in a way that induces a false sense of understanding using meaningless or misleading catch-phrases.

For a person seeking an intial understanding of entropy, they need to understand it in real-life macroscopic terms, not in terms of a theory (statistical mechanics) which they may or may not understand. Even worse, they should be induced into a false sense of understanding by using well-worn familiar words, which are ill defined and ultimately misleading.

"Entropy is a measure of the energy which is not available to do work". Does anyone ever inspect this statement? It just gets repeated over and over, because it sounds so comforting, but if you inspect it, it's worthless. Suppose I have a system with N moles of helium (a very nearly ideal gas), entropy S, internal energy U. Can anyone tell me the amount of internal energy that is unavailable to do work? No. It depends on some second system whose state is completely up in the air, and an engine to generate that work. Please lets not use this verbal tranquilizer.

The idea that "entropy is a measure of disorder" is almost as equally useless. Until one has an idea of what "disorder" means, its totally useless. To the uninitiated it means "messed up" among other things. Not very helpful, unless they understand that in this case "disorder" refers to the microscopic realm. Then they hear that a crystal is more ordered than its liquid. At equal temperatures. But what about a mole crystal of iron and a mole of water at room temperature? The iron has more entropy. And on, and on, with the but... but... but... until you finally have to explain that disorder means the Shannon information entropy and then you've left them in the dust. It's just another verbal tranquilizer.

"Entropy is the spreading of energy". Well, ok, but, not necessarily in physical space. So then we have to specify that it also "spreads" in some other statistical mechanical parameter space, and then also the exact definition of "spread" is... blah blah blah. Verbal tranquilizer.

No, for the uninitiated looking for an understanding of entropy, they have to first be confronted with its manifestation in everyday life, and that means irreversibility, the arrow of time. Videos running backward look wrong, smoke doesn't go down a chimney and form wood and air, ice does not unmelt in a glass of water, a hot pan on a stove doesn't cool down and give up its heat to the already hot burner, a stirred cup of coffee and cream does not spontaneously separate into black coffee and cream, an exploded firecracker does not spontaneously re-assemble itself. The change in entropy is a measure of the minimum amount of energy you need to put things back the way they were.

Now, armed with this intuitive understanding, they might learn some thermodynamics which quantitatively defines entropy and some statistical mechanics which explains (but does not define!) entropy, and then they are on their way.


 * Sorry to say this but I think you have fallen short of making the article clearer.

"entropy is a measure of disorder" is not usless and really is intuitive. We all have a sense of order vs disorder. Have you ever watched an apartment degrade into "disorder" and then see it "reordered?"

"For a person seeking an intial understanding of entropy, they need to understand it in real-life macroscopic terms, not in terms of a theory (statistical mechanics) which they may or may not understand." Very true, and the intuitive level is where it should start.

"Entropy is a measure of the energy which is not available to do work". That is derivative of the Britanica article and the thermodynamics text I have on my desk. Since it is explained at an engineering level it should perhaps appear later in the ariticle.

"The idea that "entropy is a measure of disorder" is almost as equally useless. Until one has an idea of what "disorder" means, its totally useless." I'm not sure that is true. Again, I think we have an intuitive sense of what is order vs disorder. We can't start an introductory article with an exacting definition of order as such borders on a epistemological level discussion of such things, which is something that might be addressed much later in the article.

You have no doubt noticed the other article once began with a definition that started with stasticial thermodynamics, which in my opinion is an exercise in pedantary. There is a tendency we have to wax pedantic about things for which we have a shaky understanding. Someone once criticized a report I wrote, "The less a person knows about a subject, the more long winded they are when writing about the subject." He was correct. The subject of Entropy is complicated to begin with and its applications and hence its definition is expanding even today. Writing a simple, clean, orderly article won't be easy. I too am hesitant to work on this but I do have a feeling for the subject and recognize when such things are well expressed, hence I do what I can. Call me vain. Zedshort (talk) 17:05, 21 October 2016 (UTC)


 * I have to agree, everyone has an intuitive sense of order and disorder, but I think this intuitive sense is limited and even misleading. If I show you two micro-snapshots of two like gases at the same density they will look equally disordered, but the one with the higher temperature has higher entropy. For two different gases as the same temperature, the one with the higher mass will have higher entropy. A mole of iron at 1200 deg C, in a beautiful crystal, will have higher entropy than a mole of water at room temperature. The essential thing about disorder is that there are many more ways to have disorder than there are to have order. But then, what do we mean by "way"? And then we are off into the realm of statistical mechanics, while the real-world, in-your-face manifestation of entropy - irreversibility - remains untouched by all of these quibbles and theories.


 * Yes, to get an even deeper understanding of entropy, you have to get into statistical mechanics. The concept of disorder is useful when talking about positional entropy, and if its made clear that this is only one leg of the elephant in the living room, then ok. But it's just counterproductive to avoid all that yucky logic and thinking and stuff in preference to a false sense of understanding using the limited intuitive concept of "disorder". PAR (talk) 03:10, 12 December 2016 (UTC)

Lede needs work
I added a sentence about disorder to the front of the lede; it was removed. The lede of this article doesn't get the job done, because it needs some kind of basic, introductory statement of what entropy is, in the first sentence, to orient the nontechnical reader for what follows. Try to imagine yourself, having no idea what entropy is, reading the first few sentences of this article. Would you not be confused and turned off to the subject matter? Beginning with the concept of irreversibility is not helpful at all if you have no idea what entropy is, even in the vaguest sense. You wouldn't want an article on velocity to begin, "The concept of time is central to understanding velocity," then going on to talk about time. This is common sense. Please someone improve the beginning of this article, if my edit that described entropy as a measure of disorder isn't good enough.  -Jord gette  [talk]  20:51, 24 December 2016 (UTC)


 * This whole article ought to be deleted. I don't know why an introduction is necessary, separate from the main article. This one reads like it should be placed on the Simple English WP, as it appears to be attempting to use Simple English, but still failing grossly. This article has almost no references, and indeed the incoherent presentation is probably out of scope of reliable references. Kbrose (talk) 22:07, 24 December 2016 (UTC)


 * Could you please read the "truly awful", "rewrite the introduction", and "entropy as disorder" threads above. It makes no sense to begin this discussion all over again from scratch. Thanks. PAR (talk) 05:43, 25 December 2016 (UTC)


 * I have read the above discussion, and I see very little discussion. It seems that one editor is trying to own the article, by making the beginning of the first paragraph adhere to the letter of the rigorous definition of entropy. In science writing this is a bad idea. Understand that we're talking about an introduction to an introduction — not a textbook treatment — so it's appropriate to start by giving the lay reader an intuitive notion of what entropy is, even if that description isn't rigorously accurate — just as an introduction to electrons would say that they "orbit" the nucleus before you get into explaining what an orbital is. This is what Zedshort means when he writes "If you want to be absolutely correct the introductory sentence would be unintelligible to all but the 0.1% of the people who come to read the article, which would be those who don't really need to read the article in the first place as they know the material." An RfD on this article would be a good idea, and I may initiate one.  -Jord gette  [talk]  03:37, 26 December 2016 (UTC)


 * I guess I am the editor you are referring to, but I am not trying to "own" the article, I'm sincerely trying to give an introductory description of entropy. It is along the lines of Lieb & Yngvason - If you want to understand entropy to begin with, you have to understand how it impacts your senses, it's real-world manifesttation. Entropy as "disorder" and "energy spreading" etc. requires an understanding of the atomic nature of matter (inaccessible to the senses) and statistical mechanics, and then, on top of that, are misleading in their vagueness and over simplification. They are not an intuitive understanding of entropy. Irreversibility is the essence of phenomenological entropy, and the statistical mechanics explains that phenomenology. I think the introduction does a fair job of describing it in that order. I don't presume to be right, I only presume to have an argument, and I would support your RFD if you thought it necessary. I mean, I have an opinion, but I am not convinced of my infallibility. I just wish anyone would look at the argument instead of taking offense at my presumed motives. Lets focus on the article, not on personalities. PAR (talk) 08:54, 26 December 2016 (UTC)

Dreadful
This article remains perhaps the worst introductory science article on Wikipedia. As a science writer, I am literally offended by its terribleness. There's almost no way to save it except to scrap it and start over. Parts of the lede paragraph are okay, then it gets way too technical for an introductory article (in an attempt to be absolutely 100% rigorous, which is inappropriate here), then there's a technical "Explanation section" which should probably be deleted altogether (I assume the regular entropy article provides one), then there is a promising "example of increasing entropy" section which is immediately made opaque to the beginner by more mathematical symbols. Then there's an out-of-place historical aside, then there's a section on "Heat and entropy" that doesn't mention entropy until the middle of the fourth paragraph, then there's another technical section not of interest to the beginner ("the energy being transferred “per incremental change in temperature” (the heat capacity, $$C_p$$), multiplied by the integral of $$\frac{dT}{T}$$ from $$T_{initial}$$ to $$T_{final}$$, is directly given by $$\Delta S = C_p \ln\frac{T_{final}}{T_{initial}}$$" — really?? In an introductory article for Pete's sake??), then there's an okay section on Introductory descriptions of entropy. In the intro we are told "All real physical processes involving systems in everyday life, with many atoms or molecules, are irreversible," and later we are told, "The equal sign indicates that the change is reversible." The next sentence, "If the temperature is allowed to vary, the equation must be integrated over the temperature path," is inappropriate for an introductory article. There is no simple fix here. It needs to be rewritten top to bottom, and I'd give it a shot, but the discussion above shows that attempts even to make moderate changes over the years have been reversed by one or two editors who seem to think it's just fine as is. There should be NO math in this article. Perhaps not even the Boltzmann equation. Technical terms should be limited strictly to those that are essential to understand the concept (such as macrostate and microstate) and explained clearly with intuitive examples. It should have a logical flow, which it doesn't. It should focus on intuitive ideas such as the melting ice, with all quasi-technical matters tied directly to such intuitive examples. Other than that, I'm out of ideas.  -Jord gette  [talk]  19:32, 27 June 2017 (UTC)


 * I suggest you activate a personal sandbox and then use it to work up an improved version of an article on this subject. When you think it is about 95% ready, use this Talk page to alert the community of Users interested in this topic and ask them to peruse your sandbox and make constructive comment. It is actually very easy and you will find others are helpful. Dolphin  ( t ) 05:48, 28 June 2017 (UTC)
 * See what you mean. At one time this article gave a gentle introduction explaining with Entropy (energy dispersal), but fans of disorder have increased the entropy, so to speak. . . dave souza, talk 13:55, 14 October 2018 (UTC)

Merge with Entropy?
Over at the talk page for Entropy, User:82.2.57.14 has made the following suggestion: "If we submit a merge request with introduction to entropy and break up section 6 then I think that's the best start. Then this article is responsible for both audiences so there's no cop out. 6.1 can join the definitions, a lot of 6.2 onwards can be merged down into 7 because "Applications" and "Approaches to Understanding" mostly mean similar things as presented here" (the section numbers refer to Entropy). I think this is a good idea. Thoughts?  Waleswatcher  ( talk ) 20:59, 27 April 2018 (UTC)

Isn’t entropy about disorganization?
I’m no scientist, but this is what my layman’s perhaps uninformed understanding was - entropy is moving from an organized state (a fuel, for example) to a disorganized one (the remains after the fuel is burned).

Also, the lede is too technical. Anything like “log(W )” is incomprehensible to me. ideisenbe (talk) 11:27, 14 October 2018 (UTC)
 * A common misconception, the Entropy (energy dispersal) approach was developed to give a better maths free explanation to laypeople. This article could do with refocussing on that educational approach. . . dave souza, talk 13:57, 14 October 2018 (UTC)


 * I disagree that "the Entropy (energy dispersal) approach was developed to give a better maths free explanation to laypeople."


 * I think that it was developed because the 'disorder' wording doesn't bear analysis as a physical concept. The 'dispersal' idea is scarcely different from the original 'disaggregation' of Clausius, and makes physical sense. Later, it was noticed to be more useful for pedagogy.Chjoaygame (talk) 17:09, 4 November 2020 (UTC)

Why not start with microstates?
Why not just go to Boltzmann’s equation straightaway? Entropy is just a count (on a logarithmic scale) of the ways some property could come to be. That is an easy concept to grasp.

How many ways are there to get a B in a course? A course with just one final exam has low entropy; a course with many tests and quizzes has high entropy. Think through the implications of the difference.

A business sells $1,000,000 of product each month. If the business makes three kinds of yacht, each costing $1,000,000, and the business can make only one yacht a month, there are only three ways they could sell $1,000,000 of product this month. Low entropy. A candy store selling $1,000,000 a month? High entropy.

In molecular physics, the items are not candy bars, yachts, or quiz scores but molecules and their energies; the macro-level state is usually temperature. Because molecules interact with each other in ways candy bars do not, there are many constraints on what the entropy can be. (One scientific law is that it always increases.) But entropy itself is pretty simple—just the number of different molecular energy configurations that could be producing a given temperature.

And because the range is so high, we use a logarithmic scale. And we add a scaling factor.

The result: Boltzmann’s equation.

No?

I’ve never taught physics, but as a student of it this seems to me more straightforward than disorder (in a special sense), dispersal (in a special sense), or unavailable energy (in a special sense). John P. McCaskey (talk) 14:44, 25 February 2020 (UTC)


 * Works for me. The question is whether it works for, shall we say, "others" who watch this article.  -Jord gette  [talk]  17:31, 25 February 2020 (UTC)


 * The Royal Society of Chemistry recommends this approach. https://edu.rsc.org/feature/what-is-entropy/2020274.article John P. McCaskey (talk) 18:21, 8 April 2020 (UTC)


 * I'm working on a video where I use a container of nails. This might be a useful example for the article, because the link between microstates and the typically thought-of concept of "disorder" is immediately recognizable.  -Jord gette  [talk]  20:27, 8 April 2020 (UTC)

I made an attempt at rewriting the beginning, in accordance with the above. For now, I used only one example, billiard balls. I would like to see some of the other intuitive examples incorporated into the article, to clarify the concepts of microstates and macrostates, including a restatement of the definition of entropy in those proper terms. I think it's a great idea to informally derive Boltzmann's equation in the manner described above by McCaskey, but not in the intro (I left that part as is for now). I decided to open with disorder, since that's by far the most common word popularly associated with entropy, before dispensing with it in favor of the more rigorous description. Let me know what you think.  -Jord gette  [talk]  17:57, 12 April 2020 (UTC)


 * To me, the change is not substantial enough. The article still says: "Think of entropy as disorder. Now let's get more rigorous on what is meant by disorder. But keep disorder as your guiding principle." But generally professors and teachers who jump right to Boltzmann's conception—let me add Moore and Schroeder, "A Different Approach to Introducing Statistical Mechanics," American Journal of Physics, vol. 65 (Jan. 1997), pp. 26-36; Kim Sharp, "Entropy According to Boltzmann"; and Kim Sharp, Entropy and the Tao of Counting: A Brief Introduction to Statistical Mechanics and the Second Law of Thermodynamics (Springer, 2019)—suggest starting with micro- and macrostates and only late in the game say, "Now that you understand entropy, here is why some people think of it as disorder. . . . If that helps you, great. If not, don't worry about it." John P. McCaskey (talk) 19:57, 12 April 2020 (UTC)
 * I removed the disorder mention from the beginning. I'd like to avoid introducing the terms microstates and macrostates in the introduction to this introduction, just to keep the material as friendly as possible. This is a tough nut to crack and there's a long way to go, but maybe it's a start. At this time, I haven't altered anything after the first four paragraphs.  -Jord gette  [talk]  22:04, 12 April 2020 (UTC)
 * Yes, I think that is better. John P. McCaskey (talk) 22:05, 12 April 2020 (UTC)

This article is an introduction to entropy. The essence of entropy is irreversibility, not microstates and macrostates, these are theoretical explanations of irreversibility. As an introduction to entropy, we need to give an intuitive, everyday understanding of irreversibility, something that somebody new to the concept can grasp on an everyday level. Thermodynamic entropy was completely defined before Boltzmann came along and explained it with statistical mechanics. Thermodynamics and statistical mechanics are two different things. Thermodynamics is a description of a thermodynamic system using thermodynamic (macroscopic) parameters, constrained by the laws of thermodynamics. You will find nothing in the laws of thermodynamics that refer to an atomic view of matter, or the statistical mechanics that go along with that assumption. Statistical mechanics is an explanation of thermodynamics. Thermodynamics can exist without statistical mechanics, but it is a collection of macroscopic measurements, again, constrained by the laws. Statistical mechanics gives you insight into why you measure what you measure. Entropy is NOT defined by statistical mechanics, it is defined by thermodynamics and explained by statistical mechanics. So it's not only bad form to imply that entropy is defined by statistical mechanics, it also takes away the fundamental intuitive understanding of entropy as a measure of irreversibility and replaces it with a theoretical explanation. Don't get me wrong, the statistical understanding of entropy is absolutely vital to its full understanding, and should certainly be developed in this article, but not in the introduction to an "Introduction to Entropy" article.

I will revert the present introduction to the previous one which stressed the intuitive understanding of irreversibility in a few days if there is no discussion. PAR (talk) 19:04, 31 October 2020 (UTC)


 * Please don't. As an introduction to entropy, the beginning of the article is presently far better than it was before. There is still work to be done, but it's no longer truly awful as many commenters over the years complained.  -Jord gette  [talk]  19:27, 31 October 2020 (UTC)


 * Ok, can you explain why it was so awful?


 * Scroll up. For years there were complaints about this article, and I don't think there have been any since the intro was re-organized. Reversibility refers to a change in entropy, so in order to understand how to get from reversibility to entropy, one has to first understand what entropy *is,* and that requires the statistical description. It's kind of like trying to explain acceleration without referencing velocity — even if one thought that "a feeling of being pushed" is a more intuitive way to understand what acceleration is, you wouldn't start off an article on acceleration as, "Acceleration refers to the feeling of being pushed." Do you have any specific suggestions for the article, other than reverting to the way you (and I think, only you) liked it previously?  -Jord gette  [talk]  16:49, 1 November 2020 (UTC)


 * I have scrolled up, reading my own comments and the comments of others, including yourself. First of all, the question is not whether the article should be the way I (and you think, only I) like it, or whether it is the way you and some people who agree with you like it. The question is what are we trying to do here? Please, please don't confuse me with a "my way or the highway" kind of editor. I have an argument, and I ask that you consider it and not react to my supposed motives. If the argument is convincing, then it is our argument. If not, then I will carry it to others, and if they disagree, so be it.
 * I think your analogy of how to describe acceleration is a good one. In an *introductory* article on acceleration, you would want to begin as if you were talking to a reasonably intelligent 12 year old, who is not yet mathematically sophisticated. Do you begin with "acceleration is the first derivative of the velocity vector with respect to time"? I'm sure we both agree the answer is "no". The statement "Acceleration refers to the feeling of being pushed", is, we both agree, not good, because it is simply wrong, its an exaggeration of what I am trying to say. But how DO you begin explaining acceleration to this neophyte? Sure, you have to start with an intuitive understanding of velocity. "How fast something is going" is close enough to begin with. Like the speedometer on a car. When you run you have greater velocity than when you walk and when you stand still, you have zero velocity. Acceleration tells you if you are speeding up or slowing down. If the speedometer goes up and up, you are accelerating and if you put on the brakes, it goes down and down and you are decelerating. If you walk and then start running, you are accelerating, etc.


 * In other words, first relate the concept of acceleration to everyday experience. Now we are ready to get more technical and mathematical. I think we should take the same approach to entropy. Without an intuitive understanding of entropy as it presents itself in our everyday life, we are just talking gobbledegook. The ESSENCE of entropy is that it manifests itself in our everyday lives as irreversibility. The most obvious apparent violation of irreversibility (using today's technology) is to run a video or a movie backwards, and see the impossible things that occur. Entropy is something that decreases in that backward movie, and increases or almost stays the same in the "real world". Now we are ready to get more technical and mathematical. Please note that thermodynamic entropy is NOT DEFINED by statistical mechanics, it is defined by classical thermodynamics, and EXPLAINED by statistical mechanics. This is as it should be. Thermodynamics defines entropy via a series of real world measurements, and the second law states that entropy is non decreasing. The development of entropy in physics follows the path we should take with the neophyte, describe it and how it impacts our senses as quantified by our measurements, then undertake to understand why it behaves that way using statistical mechanics. To start with the idea that the definition of entropy is wrapped up in microstates and macrostates and "ways of achieving a macrostate" is not only factually wrong, it is putting the cart before the horse. To get a bit more erudite, I wonder if Einstein would would agree with me? Here's a quote from Big Al himself (All emphasis mine). In this quote, consider that classical thermodynamics is a theory of PRINCIPLE, while statistical mechanics is a CONSTRUCTIVE theory.


 * "When we say that we UNDERSTAND a group of natural phenomena, we mean that we have found a CONSTRUCTIVE theory which embraces them. But in addition to this most weighty group of theories, there is another group consisting of what I call theories of PRINCIPLE. These employ the analytic, not the synthetic method. Their starting point and foundation are not HYPOTHETICAL constituents, but EMPIRICALLY OBSERVED general properties of phenomena, principles from which mathematical formula are deduced of such a kind that they apply to every case which presents itself. Thermodynamics, for instance, starting from the fact that perpetual motion never occurs in ordinary experience, attempts to deduce from this, by analytic processes, a theory which will apply in every case. The merit of CONSTRUCTIVE theories is their comprehensiveness, adaptability, and clarity; that of the theories of PRINCIPLE, their logical perfection, and the security of their foundation."


 * PAR (talk) 01:52, 2 November 2020 (UTC)


 * We'd start an introduction to acceleration article by saying it's a change in speed. Ironically your argument supports starting this article by describing entropy as a measure of disorder, which is far and away the most intuitive way to describe what it is. It's kind of crazy that the article doesn't start this way, but you have been so insistent over the years that it not start with disorder, so the compromise was made that it start with microstates instead. But, I am 100% against starting with reversibility, because the article needs to start out by describing what entropy is, not by how its change can be recognized. If it were up to me, the article would start by saying that entropy can be informally described as a measure of disorder; maybe then reversibility could be invoked, followed by the more rigorous current description of entropy in terms of microstates (without using that word). Is that preferable to you?  -Jord gette  [talk]  16:14, 2 November 2020 (UTC)


 * I understand that this is what you want, but in order for us to have a discussion, please explain where my argument is flawed or faulty. If we simply go back and forth with "I want this" and "I want that", we will get nowhere. Please critique my argument. Do you understand my point that thermodynamic entropy is not defined by statistical mechanics? That statistical mechanics is a constructive theory which explains it, but does not define it? Do you understand my point that this article is about thermodynamic entropy and not information entropy, that information entropy is just a means of understanding an already-defined thermodynamic entropy?


 * Your statement "the article needs to start out by describing what entropy is, not by how its change can be recognized" baffles me. The only way we know what it IS is to measure it. In order to understand it, we build a constructive theory which may or may not be right, (so far it is very excellently right) and then draw analogies to information entropy. Analogies that wander away from the information entropy explanation, like entropy as disorder, energy spreading, etc. are, upon closer examination, vague, empty or downright wrong. If we want to understand information entropy, then the idea that it is a measure of what we don't know is the best I have found. It doesn't fail and it doesn't logically chase its tail.


 * Ok, let's look at the idea of (information) entropy as disorder. It's obviously meaningless until we define "order". Take a pack of cards and put them all in order, clubs, diamonds, hearts, spades, ace, 2, 3... King for each. We can call that "ordered". Then shuffle the deck thoroughly. Now its disordered. The information entropy at the beginning was zero, not because it was in a particular order, but because we knew where every card was. The entropy of the shuffled deck is high. Measured in bits, its about Log2(52!)=225.6 bits where Log2 is logarithm to base 2. The reason the entropy is high is not because it is "disordered" but because we don't know where any particular card is. Suppose I take that shuffled deck and mark down the position of every card, and declare that to be "ordered". Then I shuffle the deck and by some miracle, it winds up being in the order clubs, diamonds, hearts spades, ace, 2, 3... etc. The entropy of that deck will again be 225.6 bits. This is not because of its order, but because we don't KNOW that it is so ordered. Information entropy is a measure not of disorder, but of what we don't know. One favorite example is the idea that a messy desk has higher entropy than a neat desk. There are many more ways to have a neat desk than a messy desk and information entropy is the log of the number of ways. But if I take a "messy" desk and write down the position and orientation of every paper clip, potato chip, crumpled up piece of paper, etc., and then call it my "standard desk", then there is only one way for that desk to be in that condition and the entropy is zero. There are many ways to make a neat desk compared to the one way to make my standard desk, and we don't know the position and orientation of these various "neat" desks, and so the entropy of a "neat" desk is higher. Again, its not a matter of some arbitrary definition of "order", it's a matter of what we don't know.


 * If you want to define entropy as a measure of disorder, you have to tie down exactly what you mean by "order", and once you do, when you measure the information entropy of any other state, you are in fact measuring what you don't know about that state, compared to the fact that you know everything about the "ordered" state. In other words, the degree of disorder is identical to the information entropy, and at best, you have simply used two different words to describe the same thing, while "disorder" is less informative and more misleading than "a measure of what we don't know".


 * Also, the rather vague statement "measure of what we don't know" can be quantified explicitly. The entropy of a shuffled deck is 225.6 bits, and that is the average number of carefully considered yes-no questions you have to ask in order to determine the position of every card in that shuffled deck. You could say that the entropy of that shuffled deck is 225.6 yes-no questions, the entropy of your "ordered" deck is zero yes-no questions.


 * So now back to thermodynamic entropy - it is the result of a series of scientific measurements based on the theory of classical thermodynamics. That's what thermodynamic entropy IS. In thermodynamics, we cannot measure absolute entropy, we can only measure it's change. It is not a coincidence that this change is the only manifestation that entropy has on our senses, and by our senses I mean yes, the pondering of the backward movie, but ultimately it also means our careful measurements. Now Boltzmann comes up with a link between thermodynamic entropy and information entropy by postulating a whole list of things, like the atomic theory of matter, macrostates, microstates, equal apriori probability of microstates, etc. etc. In other words, he comes up with the constructive theory of statistical mechanics hoping it works, and it does! So this link to information entropy, along with all these assumptions, allows us to gain a deeper understanding of thermodynamic entropy. But they do NOT define it. The thing that bothers me is the mushing together of the two theories and thinking that information entropy defines thermodynamic entropy, and even worse, the idea that "entropy as disorder" adds to the understanding, when in fact it detracts from understanding and, even worse than that, the idea that entropy is a "spreading of energy" which is flat out false, as shown by the entropy of mixing.


 * May I ask that you please critique the above argument as well? Offer any counter arguments? PAR (talk) 04:05, 3 November 2020 (UTC)


 * Do you understand my point that thermodynamic entropy is not defined by statistical mechanics?
 * It doesn't matter. This is an introductory article for laypersons. Such rigor need not determine how the topic is presented in the first few sentences. The only goal is to give the reader something relatable to grab onto. This is indeed the challenge of science writing.
 * Ok, let's look at the idea of (information) entropy as disorder. It's obviously meaningless until we define "order".
 * Nonsense. As editor Zedshort put it above: Again, I think we have an intuitive sense of what is order vs disorder. We can't start an introductory article with an exacting definition of order as such borders on a epistemological level discussion of such things, which is something that might be addressed much later in the article. Correct me if I'm wrong but I think you're the only one who has made the argument that we can't start with disorder, even though that's an extremely common device employed in definitions of entropy. Consider this, this, and this . All of these definitions mention order/disorder by the second sentence. (This being an introductory article, I think it's a bad idea to start with unavailable energy.)
 * In science writing, one always gives up some rigor, at least initially, to help the reader work through a difficult concept. When introducing the concept of electrons in an atom to laypersons, you don't start with quantum mechanics and probabilities; you start with the device of electrons "orbiting" the nucleus. There is nothing wrong with that. You don't have to define "orbit" in that context. This is simply the stepwise manner in which a difficult science concept is most effectively and least confusingly communicated to laypersons.
 * The thing that bothers me is the mushing together of the two theories and thinking that information entropy defines thermodynamic entropy
 * Since this is an introduction to entropy and not the main entropy article, with all due respect I think you need to let go of your desire to have perfect rigor in the beginning of the introduction. There is plenty of room later in the article to recover the rigor. But the beginning of the article needs to give the lay reader some intuitive conception of what entropy is. I thought that the billiard table did that as an alternative to order/disorder — as a compromise to you — but upon further review, maybe that misses the forest for the trees and we should just go with order/disorder.
 * Again, I invite you to make specific suggestions about how to begin the article rather than making the same rigor-oriented arguments. I think we should start the article by going right to order/disorder, and then go immediately to reversibility. If this is unacceptable to you, then I think we've reached an impasse and need to do an RfC. I'm not interested in continuing to go around in circles.  -Jord gette  [talk]  17:09, 3 November 2020 (UTC)


 * I agree with you, this needs to go to an RFC. Let the larger community judge our arguments, mine are laid out fairly well above, I think. I will begin the RFC, stating the problem as neutrally as I can.


 * "The only goal is to give the reader something relatable to grab onto". Yes, and that's exactly what I am trying to do by using a backward movie to illustrate the essence of thermodynamic entropy, that it is a number that goes up in the forward movie, down in the backward movie, and the impossible things that would happen if entropy did not increase or at least stay the same. If they grab onto the idea of information entropy as disorder, and continue to study entropy, they will eventually have to let go of it, so why give it to them in the first place? The idea of information entropy as a measure of what we don't know is just as relatable, and further study will only expand and refine that concept.


 * "Again, I think we have an intuitive sense of what is order vs disorder. We can't start an introductory article with an exacting definition of order ...". My point is, again, that this intuitive sense of order is misleading. We have an intuitive sense that a moving object slows down and comes to rest. That intuition has to be questioned, then we can understand Newton's law that a body in motion tends to stay in motion, then we can introduce the slowing down as being due to friction. The intuitive sense of order does NOT always imply a lower entropy. The information that is available by having intuitively ordered configurations is the essence of the information entropy, and our intuitive sense of order does not always guarantee that knowledge. We will ultimately have to reject our "intuitive sense of order" in order to understand entropy, so why give it to them in the first place?


 * I do not desire to have perfect rigor, I agree that a certain lack of rigor to begin with is likely necessary in order to give the neophyte something to, as you say, "grab onto". But the idea of a backward running movie, ice freezing in a glass, milk unmixing in coffee and jumping back into the container are not what I would call rigorous. The idea that entropy is a number that never goes down in the real world, but goes down in a backward movie is not what I would call rigorous. The idea that Boltzmann discovered that by looking at a thermodynamic system as a bunch of particles about which we know very little and, by using what are now known as information-theoretic concepts, found a relationship between thermodynamic entropy and information entropy. And now we can go into information entropy, since Boltzmann showed that it was very important. This does not sound like fanatic rigor to me, its just simple truth. PAR (talk) 22:10, 3 November 2020 (UTC)


 * ''Yes, and that's exactly what I am trying to do by using a backward movie to illustrate the essence of thermodynamic entropy
 * And that's great once we've given the reader an idea of what entropy is. Are you suggesting that the article begin with "entropy is a number that goes up in a forward movie"? I'm asking this because you still haven't given any specific suggestions of how to start the article.
 * We will ultimately have to reject our "intuitive sense of order" in order to understand entropy, so why give it to them in the first place?
 * For the same reason that an article for laypersons on quantum superposition might initially say that a particle can be in two places at once. Or that an article for laypersons on gravity might initially say that gravity is a force that draws objects together. You give the reader a simple picture to start with, and then you refine from there. It's just how clear science writing works.  -Jord gette  [talk]  00:11, 4 November 2020 (UTC)


 * "Are you suggesting that the article begin with "entropy is a number that goes up in a forward movie"?" - No, not that quickly, but ultimately yes, up in a forward movie, down in a backward movie. Then say that the backward movie is impossible, so it is impossible for entropy to decrease. This illustration is included among other illustrations that are mentioned. You keep talking about what THERMODYNAMIC entropy IS. What I am saying is that what it *IS* is inextricably tied to the idea of irreversibility. INFORMATION entropy is something else. It is a very valuable something else, but still something else. Pouring cream into coffee, and mixing it causes the thermodynamic entropy to increase. The whole process could occur backwards without violating any other law of physics except the 2nd law of thermo, and clearly that never happens. The second law states that it will never happen because that would entail a reduction of entropy, which is impossible. Other examples were also included, like you can't unscramble an egg, etc. All these examples serve to give an intuitive idea of thermodynamic entropy by illustrating irreversibility.


 * I have resisted giving specific suggestions because I thought if we could come to an understanding first, the suggestions would be obvious. Anyway, I think the article should start out by giving the above mentioned description and examples of (the change in) thermodynamic entropy. Then bring in Boltzmann who explained this relentless increase by viewing the system as a bunch of atoms or molecules, and realizing that the system of particles can have all sorts of different velocities and positions, but the vast majority of these situations all look the same to us. As things settle down, the system assumes its most probable appearance. Before that happens, we have a highly unlikely situation which looks different to us. The former situation has high information entropy, the latter is low. Now we can introduce the concepts of microstate and macrostate, and say it again, more clearly.


 * If I had my way, we could explain why entropy is sometimes thought of as disorder, or energy spreading, (especially the cream in the coffee example) and then point out why these are ultimately vacuous or misleading, steering the neophyte away from these unfortunate concepts right from the get-go, but I'm afraid that would offend too many people who prefer to explain entropy as they learned it, rather than to critically study it (There I go, being vain and arrogant again, sorry :). This is not fanatical rigor. The idea of information entropy as a measure of what we don't know is very approachable, and the fact that is correct is just a bonus.


 * Anyway, at that point, we are off and running with information entropy and how it explains thermodynamic entropy, stressing that information entropy is a measure of what we don't know about a system, and that the increase in thermodynamic entropy is ultimately an increasing loss of our ability to predict the future on a thermodynamically microscopic scale. In other words, it is a loss of information, which is an increase in what we don't know about that system. PAR (talk) 03:14, 4 November 2020 (UTC)

Technicality
I have to say, I LOLed at the technical maintenance tag right below the introductory article one. I might go so far as to say that entropic forces push pages toward an overly technical state. &#123;{u&#124; Sdkb  }&#125;  talk 00:20, 7 June 2020 (UTC)

RfC about the most useful introduction to the "Introduction to entropy" article.
How should the introductory article on (thermodynamic) entropy begin? Order/disorder? Macro/Microstates? Irreversibility? etc.?

There are two introductions upon which we cannot agree. The present introduction is one, the second is the version of 24 January, 2020. Arguments are presented in the above sections, especially the previous section. PAR (talk) 22:10, 3 November 2020 (UTC)


 * A diversity of opinion or interpretation here.


 * Nowadays, there are two mainstream definitions of absolute temperature, both purporting to define a measurement, one from traditional thermodynamics, the other from statistical mechanics as recently ordained by IUPAC.


 * Correspondingly, there are two mainstream definitions of entropy in physics, as a thermodynamic quantity, and as a statistical mechanical quantity as proposed by Boltzmann.


 * Since 1949 (Shannon) there have been two mainstream notions of entropy, as a quantity in physics, and as a quantity in information theory. Shannon's definition measures the length of the most condensed possible code in a defined context.


 * Nowadays, there are two mainstream intuitive interpretations of physical entropy, one traditionally since Boltzmann, as disorder, and the other, since Guggenheim (1949), as spread or dispersal, which is scarcely distinguishable from Clausius's notion of disaggregation, the opposite of condensedness. Of these, the Boltzmann interpretation as disorder is more widely cited, though not, in my opinion, adequately argued for.


 * I don't feel helped by the saying that physical entropy is about irreversibility. I think it is more important to say that it characterises states of thermodynamic equilibrium, which maximise the dispersal of energy.


 * Likewise, I don't feel helped, for a physical context, by the saying that information entropy expresses what we don't know. I think it more helpful in physics to say that "quantity of information" is about expression with greatest possible concision or condensedness.


 * I think that Wikipedia should recognize all the mainstream conceptions.


 * My take on this is that entropy is dispersal. This integrates the range of the diversity.Chjoaygame (talk) 15:51, 4 November 2020 (UTC)


 * Then how do you explain the entropy of mixing, in which there is no energy dispersal? PAR (talk) 03:32, 5 November 2020 (UTC)


 * A valid question that deserves a careful response.


 * Entropy of mixing refers to a process. In order to define the particular process precisely, the conditions of the process need to be specified.


 * Because of its experimental convenience, the usually or conventionally chosen condition of 'entropy of mixing' is of constant pressure and constant temperature; with this choice, indeed as you indicate, the entropy of mixing is usually non-zero. This seems to establish the case that is being proposed.


 * One may consider more closely the case for the conventional definition. The process is conducted by holding the pressures of the system and of the relevant part of the surroundings constant. Initially, the two bodies of matter are juxtaposed, but separated by an impermeable wall. Beyond this, the other walls are impermeable, and immovable except insofar as they need to be moved in order to maintain the constancy of pressure. The thermodynamic operation of removal of the separating wall is imposed. The volume of the system is increased by the volume added from the surroundings. The matter of the system disperses or spreads itself into the newly accessible volume. Likewise the matter added to the system from the surrounding disperses or spreads itself into the newly accessible initial volume of the system. Usually then the entropy increases. This justifies the idea of positive 'entropy of mixing', through spread or dispersal.


 * But, as remarked by Gibbs, mixing can be conducted under other conditions. In particular, one may require that the process be conducted under constant volume of the system, as for example is chosen in the definition of internal energy, with all the state variables being extensive: $$U(S,V,{N_j})$$. With this definition, the added or mixed matter is forced infinitely slowly, so as prevent significant frictional heating, through the newly permeable wall into the system from the surroundings without change of volume of the system. As remarked by Max Born, with other walls of the system being impermeable and immovable, there is no heat transfer in this process; the whole process is of matter transfer. In this case, when the matter of the system and the matter added from the surroundings are both ideal gases, then, as Gibbs remarked, the entropy of mixing is zero. This is because in ideal gases the only interaction between the gas molecules is elastic collision; there is zero potential energy of interaction between the molecules. In this kind of process, entropy of mixing is determined only by intermolecular potential energy.


 * I think this answers the question.Chjoaygame (talk) 04:30, 5 November 2020 (UTC)


 * I will post a response to your talk page, because this discussion will get technical and distract from our purpose here. If we come to an agreement, then we can give a short post here. PAR (talk) 13:17, 5 November 2020 (UTC)


 * I think it is important to maintain the difference in level between this article and the more detailed article on Entropy. Yes, Wikipedia should recognize all the mainstream conceptions, but not necessarily in this article which is advertised as for beginners since Wikipedia does also have the other article. So I think this article should basically be left as is: we explain the Carnot-Clausius concept and mention the Boltzmann concept briefly. For completeness we could add a brief section on the Shannon concept, but I would keep it to a few lines plus a note at the beginning saying Main article: Entropy. Dirac66 (talk) 03:13, 5 November 2020 (UTC)


 * I am inclined to think that Wikipedia is an encyclopedia, not primarily a work of pedagogy for beginners. A primarily pedogogical article is an invitation to unbridled editorial opiniation.Chjoaygame (talk) 04:40, 5 November 2020 (UTC)


 * The present article begins with the statistical mechanics macrostate/microstate explanation of thermodynamic entropy, and then in the second paragraph actually addresses thermodynamic entropy and its manifestation as irreversibility. I think this is backwards, and I also think it is wrong to imply that statmech defines thermodynamic entropy. It doesn't, it explains it. PAR (talk) 03:33, 5 November 2020 (UTC)


 * Agreed that statistical mechanics explains thermodynamics when the molecular mechanism is precisely known. When it is not precisely known, then statistical mechanics is a wishful program, not a precise explanation.Chjoaygame (talk) 04:40, 5 November 2020 (UTC)

A few comments:
 * I think the readers would be served best if we limit the scope of this article to physics (statistical mechanics/thermodynamics), and leave the Shannon/information theory to be covered elsewhere. Equating the two together is controversial, but more importantly it seems very confusing to be drawing parallels between statistical mechanics and information theory in an introductory article.
 * I concur with PAR that it would be better to introduce the macroscopic thermodynamics picture first, and only go on to a discussion of microstates and statistical mechanics once the intuitive concept is clear. This is both how the concept developed historically, and how it is usually taught pedagogically.
 * We should give a presentation which has the broadest support in the reliable sources, rather than trying to personally judge about which definition is ultimately the best. Most importantly, cite a source to back up your explanation, not just general references to the concept of entropy. I find Kittel and Kroemer's (Thermal Physics, 2nd edition, pp.42) statistical mechanics explanation is pretty decent second step after the macroscopic picture has been introduced: "entropy is defined as the logarithm of the number of states accessible to the system". The article is pretty light on references at the moment; let's try to bring more WP:RS to the table rather than trying to determine the best approach from first principles. &#12296; Forbes72 &#124; Talk &#12297; 06:53, 5 November 2020 (UTC)


 * While it is necessary to rely on reliable sources, I think the present problem has only such a wide range of reliable sources that the reliable source principle is inadequate. That is one reason why this article is an invitation to unbridled editorial opiniation.Chjoaygame (talk) 07:32, 5 November 2020 (UTC)


 * @Forbes72: I think we can view Boltzmann as pioneering the use of primitive information theory concepts before it was formally known as information theory. In other words, I think that a wall between statistical mechanics and information theory is artificial. Statistical mechanics is the application of information theory to thermodynamics. Sure, this does not mean that we dive into theoretical information theory to begin with, so in that sense I agree with you. I also agree that references are necessary, but as Chjoaygame says, there are "reliable sources" that conflict, and we need to be careful of "unbridled editorial opiniation (sic)". I would strongly object to Kittel and Kroemers statement as a "definition" of entropy. How can you have two definitions unless there is a mathematical proof that they are equivalent? No such proof exists. As references to support this I would offer Jaynes ( see Maximum entropy thermodynamics) and Lieb & Yngvason.


 * Anyway, the bottom line is how do we *introduce* someone to the concept of thermodynamic entropy, without assuming prior knowledge other than everyday experience, or a degree in mathematics? I think the principles we should follow are simplicity, accessibility, non-fanatic accuracy, and if there are two explanations that are roughly equally simple and accessible, we choose the one that is least likely to lead the reader into vacuous or false concepts that will later have to be discarded. I recommend that that be our unbridled opinion, beyond that I'm open to suggestion. PAR (talk) 13:18, 5 November 2020 (UTC)
 * I agree with both of you that the hardest part here is dealing with different presentations in different sources. I generally agree with your principles, PAR. Let's discuss the details then. Jaynes' 1957 paper has "In this paper we suggest a reinterpretation of statistical mechanics which accomplishes [viewing thermodynamic entropy and information theory entropy as the same concept] so that information theory can be applied to the problem of justification of statistical mechanics". In another part "we can derive the usual relations in a very elementary way without any consideration of ensembles or appeal to the usual arguments concerning ergodicity or equal a priori probabilities." Both statements clearly recognize the consensus presentation of entropy does involve ensembles and ergodicity. Jayne's view has some support in the literature, but is clearly a minority interpretation. I assume by Lieb & Yngvason you're referring to chapter 8 of Entropy, but the chapter is about 50 pages long - I'm not sure what part you are referring to specifically.


 * I don't think we need to prove definitions are equivalent to include them, only that the notions are not contradictory. For example, gravitational mass and inertial mass are treated as the same thing, even if there is no generally accepted proof the two different definitions are identical. The standard on Wikipedia is that the definition is given in reliable sources. Do either of you think Kittel/Kroemer's definition contradicts anything else written in the article? I'm not trying to insist on a particular definition, but I want to better understand the objection. &#12296; Forbes72 &#124; Talk &#12297; 19:07, 5 November 2020 (UTC)


 * Part, but not the whole, of the "standard" in Wikipedia is verifiability from reliable sources; definition is not explicitly distinguished in that "standard". Our problem is that diverse reliable sources use different definitions, based in different universes of discourse. Since they are from different universes of discourse, it hardly makes sense to try to decide whether they contradict each other. A related problem is that IUPAC has now officially established a definition of temperature that by strict thermodynamic logic is an empirical definition, and by statistical mechanical reasoning is an absolute definition.Chjoaygame (talk) 04:48, 6 November 2020 (UTC)
 * What if we state in the introduction there are three different definitions based on the articles which already exist: Entropy (classical thermodynamics), Entropy (statistical thermodynamics), and Entropy (information theory). We could organize separate sections to introduce each point of view, and then a section about discussing their relationship. The thermodynamic definition and the statistical definition are generally thought to be compatible, but it has not been definitively proven that they are equivalent, and the information theory definition has been suggested to be the same (e.g. Jaynes) but this view is contentious. &#12296; Forbes72 &#124; Talk &#12297; 18:26, 6 November 2020 (UTC)


 * I think the statistical thermodynamics entropy is just the information entropy as applied to a physical system of particles, along with a number of assumptions about that system (equal apriori probability of microstates, etc.) Thermodynamic entropy is defined as the result of phenomenological thermodynamic measurements, an entirely different animal. If you mean by "compatible", that statistical thermodynamics succeeds in explaining thermodynamic entropy, then I agree, but statistical thermodynamics does not define thermodynamic entropy, thermodynamics defines it. Statistical thermodynamics essentially defines information entropy as it applies to the system, and Boltzmann linked the two with his famous equation. That linkage is not a mathematical identity, it is a condensation of a number of assumptions coupled with experimental facts which has proven to be very successful. Nevertheless the two entropies remain distinct.


 * The two entropies are connected by Boltzmann's famous equation S=k ln(W), where W is the number of microstates comprising the macrostate. If you can stick with the following argument, it is very instructive, I think. Boltzmann's ln(W) uses the natural logarithm. If we use base 2 logarithms (Log2(W)), then the logarithmic term is measured in bits and you use a different Boltzmann constant: S=(k Log[2]) Log2(W). When you measure information entropy in bits, it is equal to the average number of optimally chosen yes-no questions you have to ask in order to determine the microstate from the macrostate. For example, if you have a shuffled deck of cards, each card equally likely to be at any particular position in the deck, then there are 52! equally possible "microstates" of that deck, and the information entropy is Log2[52!] which is about 225.6 bits. That means you have to ask, on average, 225.6 yes-no questions to determine the exact ordering of the shuffled deck. (top card, question 1: is it red? no? ok, its black. question 2: Is it a spade? Yes, ok its a spade, etc. etc.)


 * This means that the phenomenological thermodynamic entropy is equal to k Log(2) times the number of yes-no questions you have to ask about a thermodynamic system, knowing its macrostate, in order to determine its microstate. While this is not a proof of anything, I think it clearly illustrates that Boltzmann was essentially using, perhaps inventing, certain aspects of information theory, before it was formalized as such, to deduce his equation.


 * Again, using the principle that we do not lead a new reader down a path that will ultimately have to be abandoned, unless it is absolutely necessary to sort of bootstrap their understanding, I think that "entropy as disorder", and "entropy as energy spreading" are counterproductive. In an introductory article, we can mention it, because it is so "mainstream", but at least let's not present them as the key to understanding thermodynamic entropy. I feel the same about introducing three different definitions of thermodynamic entropy. Unless there is a mathematical proof of their identity, that is logical nonsense. PAR (talk) 13:05, 7 November 2020 (UTC)


 * The title of the article doesn't restrict it to thermodynamic entropy. The article does at present include statistical mechanical and informatic entropies. I think the latter two are not thermodynamic entropy. I think there are three (at least) radically distinct concepts of entropy, and that the article, if it mentions them, should emphasise their radical distinctness.Chjoaygame (talk) 14:39, 7 November 2020 (UTC)
 * Fully agree that statistical mechanics and information theory entropy should be clearly marked as distinct concepts rather than mixed into the basic definitions of the thermodynamics. It's interesting to explore the connections between fields, but to start out, it would be better to stick to only what is absolutely necessary to explain the basic concept of thermodynamical entropy, since it is confusing to have an introduction that jumps between so many concepts.&#12296; Forbes72 &#124; Talk &#12297; 20:39, 10 November 2020 (UTC)

As the person who suggested this RfC, I am disappointed that this discussion is getting weedier and weedier rather than the opposite. Let me quote two comments from this page, above, that I hope will make a dent:


 * Please try to word the entry so that someone who doesn't understand physics at all, or at least only the very basics of physics--like high school physics, or even better, middle schoolphysics--can understand it. If that isn't possible, try to make a clearer path of the necessary research that needs to be done to understand it.


 * I am saddened to look on as this site becomes so useless to me and my youngsters that I no longer direct them here for any meaningful information in the sciences. Hopefully, the ego inflation of the collective "authors" was worth the deprecation in value, and ultimately, the demise of this site. But please, carry on blathering about the Clausius and Boltzmann equations. We shall all sit by silently as you dazzle us with your expertise... and we learn nothing.

Could it be that it's just not possible to present a comprehensive article on entropy for laypersons? Perhaps the topic is just too abstruse and convoluted. Others have suggested that the article be deleted. I disagree, but I want an article that unapologetically gives up as much rigor as necessary in order to give the reader some idea of what entropy is in the broadest sense. No math, no jargon. Just a crude sketch. It's "Introduction to Entropy" — it is not and should not be "All aspects of entropy explained completely and fully, but for laypersons." Arguably, that's what the main article should be! Can we please get some movement in this direction?  -Jord gette c [talk]  23:27, 7 November 2020 (UTC)


 * As I understand it, Wikipedia intends to be an encyclopaedia. As I read him,  -Jord gette  would like it to serve another purpose as well: a short cut for children to what in the past has been university science.Chjoaygame (talk) 00:46, 8 November 2020 (UTC)]


 * I agree with Jordgette's sentiment 1000 percent, in principle. The question is not "do we sacrifice rigor", but rather "which rigor and how much of it do we sacrifice". I think introducing a reader to THERMODYNAMIC entropy, which is what this article is about, by way of irreversibility is both simple, intuitive, and rigorous. The backward movie, the cream in the coffee, the smoke down the chimney, these are all simple, rigorous and intuitively instructive examples of THERMODYNAMIC entropy change. To say that THERMODYNAMIC entropy goes up for these irreversible processes, and would go down if they were reversed, does not involve a lot of jargon and math. To then pose the question of "why is this so?" is not troublesome. Now we introduce a guy who figured it out, by the name of Ludwig Boltzmann and the name of his theory is statistical mechanics. Next we can give as simple an explanation of Boltzmann's insights as we can, sacrificing any rigor that is necessary, and refusing to sacrifice rigor when it does not cloud the new reader's understanding. "disorder", "spreading", "what we don't know", these are all in the realm of Boltzmann's answer to "why is this so?", because they involve Boltzmann's assumptions of the atomic theory of matter (not a tough thing to describe) and equal apriori probability of microstates (much stickier, but approachable by some simple examples). Can we introduce these concepts in a simple way, and discuss their advantages AND limitations?


 * I think that any description of statistical mechanical entropy that relies on the idea of "disorder" without defining "order" is dead in the water. When "order" is defined, it boils down to low information entropy. So why bother? I think the idea of "energy spreading" is demolished by the entropy of mixing example, but the idea of "spreading of energy or mass" may have some merit.


 * Also, the implication that people who jump to inappropriate rigor and complication are trying to inflate their ego or self-promoting their own wonderfulness, bothers me. Maybe they are just failing in their sincere attempt to inform. That's why focusing on the argument and not on personalities is the path through this jungle. PAR (talk) 02:20, 8 November 2020 (UTC)


 * I don't know the rules about changing the title of an article. Does one change the title, or delete and re-create? If this article is about THERMODYNAMIC ENTROPY, could it be re-titled Introduction to thermodynamic entropy? I favour doing so if the article is to be oriented by the thermodynamic concept.


 * As for statistical mechanical entropy, the mathematical formulas are generally agreed.


 * As for the Shannon 'entropy', again the mathematical formulas are generally agreed.


 * An ordinary language interpretation, or several ordinary language interpretations, that may or may not integrate the three threads, is not so easy, but it may be what  Jord gette  is asking for above all.Chjoaygame (talk) 02:55, 8 November 2020 (UTC)


 * Further comments


 * Editor PAR writes "I think that any description of statistical mechanical entropy that relies on the idea of "disorder" without defining "order" is dead in the water." I agree. But it puts us in the gunsights of diehard Boltzmann anti-Clausius traditionalists, who have significant weight of traditional sourcing. They say that 'order' has "intuitive meaning", or somesuch, and doesn't need definition. I think they are off-beam, but I guess they have clout.


 * Editor PAR continues "When "order" is defined, it boils down to low information entropy." If we can agree to move on, from Boltzmann's ordinary language interptretation as 'disorder', into the twentieth century, we can avoid the question of whether 'order' boils down to 'low information entropy'.Chjoaygame (talk) 03:52, 8 November 2020 (UTC)


 * An item of history. Guggenheim (1949) wrote


 * "To the question what in one word does entropy really mean, the author would have no hesitation in replying 'Accessibility' or 'Spread'. When this picture of entropy is adopted, all mystery concerning the increasing property of entropy vanishes. The question whether, how and to what extent the entropy of a system can decrease finds an immediate answer."


 * "If instead of entropy one reads number of states, or spread, the physical significance becomes clear."


 * ""If then we observe a change taking place in a system which appears to be isolated we may be sure that it has not been isolated very long. Such changes as we observe are manifestations that the system is spreading itself over states now accessible, but until recently inaccessible. They have been made accessible by some agency external to the system."


 * For me, Guggenheim is a reliable source. So far as I know, Guggenheim doesn't say whether it is energy or matter or both that spread. He settles for number of states. That puts him very close to statistical mechanic Boltzmann with his mathematical formula for 'entropy'. And I think not too far from thermodynamicist Clausius with his 'disaggregation'. 'Number of states' is a high abstraction, less intuitively or physically concrete than 'spread of matter or energy'. But, even so, I think 'spread' has merit for our purposes. Simple and intuitively evident examples can exemplify spread of matter or of energy interpreted as spread over an abstract 'space' of microscopically specified states.


 * Another item of history. It is folklore and perhaps, for all I know, fact, that Shannon was searching for a name for his information theoretic quantity. Von Neumann suggested 'entropy' because he said that no one knows what 'entropy' means, and using it would put Shannon at an advantage in a debate.


 * Often it is said that Shannon's quantity, based in coding theory, expresses "quantity of information". For me, especially in the present context, that is not a very good way of speaking. I prefer to think in terms of concision or condensedness, or, contrariwise, of prolixity,  extent, or spreadedness of coded expression, which can be found in Shannon's writings, as well as in more recent sources. For me, that lines up neatly with the Guggenheim–Clausius interpretation. For a fan of Jaynes, such as myself, the 'weight of evidence' interpretation is valuable, but in this context I think 'focus of evidence' or 'intensity of evidence' would be practically equivalent and good.Chjoaygame (talk) 05:23, 8 November 2020 (UTC)
 * Late update: informatic entropy is a measure of diffuseness, unfocus, scatteredness, or cloudiness of evidence or expression. I think these near synonyms of 'spread' fit coded information better than does 'spread' itself. Focus and intensity belong to negentropy, though we will likely not use that word.Chjoaygame (talk) 02:25, 9 November 2020 (UTC)


 * @Chjoaygame:


 * 1) Renaming the article is a good idea.
 * Ok.Chjoaygame (talk) 07:01, 8 November 2020 (UTC)


 * 2) Let's ignore the traditionalists. If they have no argument, they have no clout. Intuitive idea of disorder is nonsense without an idea of order, and an appeal to an "intuitive sense of order" is not scientific, plus the intuitive sense of order can give the wrong answer. Which is more ordered, a one-mole perfect crystal of tungsten at 2000 degrees F, or a one-mole bowl of water at room temperature? The tungsten has the higher entropy.
 * I am not too sure about clout. I have in the past done some counting of reliable sources.Chjoaygame (talk) 07:01, 8 November 2020 (UTC)


 * 3) I think the spread of mass OR energy is not bad, but I think it has its exceptions as we have discussed.
 * I would go for 'spread' in the abstract 'space' of states as the principal idea, with more physically apprehensible partial examples from spreads of matter or energy.Chjoaygame (talk) 07:01, 8 November 2020 (UTC)


 * 4) Entropy as a measure of what we don't know is quite rigorous, yet a simple concept. I have to agree, it provides less immediate intuitive insight into the physics of thermodynamic entropy than the spreading concept.
 * I am not too comfortable with talk of what we know. The logic of operators such as 'it is known to ... that ...' is a tricky topic in the universe of 'possible worlds' theory, also known as modal logic. I would favour the idea of more or less condensed, focused, or aggregated evidence or brief encodability.Chjoaygame (talk) 07:01, 8 November 2020 (UTC)


 * So I propose the introduction to be as follows: First, everyday examples of thermodynamic entropy change, including the cream in the coffee, the hypothetical backward movie, etc., etc. Then we pose the problem "why does it behave this way" and then we go into Boltzmann's explanation without a lot of math and jargon, eventually winding up with macrostates, microstates, etc. Then we describe approaches based on spreading, disorder, lack of information, listing the advantages and disadvantages of each. PAR (talk) 06:22, 8 November 2020 (UTC)


 * When you write of "the introduction", are you referring to the article Introduction to thermodynamic entropy as a whole, to the lead of the article, or to a section of the article headed 'Introduction'?Chjoaygame (talk) 11:41, 8 November 2020 (UTC)

All of this typing by great minds, and we're still not one bit closer to figuring out how to do the first paragraph.


 * I propose the introduction to be as follows: First, everyday examples of thermodynamic entropy change

So you propose that the first sentence of the article on Introduction to thermodynamic entropy be something like, "Here are some examples of thermodynamic entropy change"? It's almost comical how we've come back to the beginning of this discussion.  -Jord gette  [talk]  19:41, 8 November 2020 (UTC)


 * @Jordgette: Please stop with the "great minds" sarcasm. We are simply trying our best to solve the problem that you have identified and that I (at least) agree with, which is "how do you introduce the concept of thermodynamic entropy and its statistical mechanical explanation to the lady that you mentioned and her youngsters?". If we have a choice between being rigorous yet simple and informative or being wrong and giving a false feeling of being informed, I say we choose the latter. So we argue about esoteric stuff with that idea always in mind. So yes, I propose that the first sentence(s) of the article on Introduction to thermodynamic entropy be something like, "Here are some examples of thermodynamic entropy change"? Because that is what THERMODYNAMIC entropy IS. This is an intuitive, simple and true introduction to the concept of THERMODYNAMIC entropy. All of the spreading, disorder, what we don't know stuff falls under the heading of "Here is how Boltzmann EXPLAINED thermodynamic entropy". You don't teach someone to drive a car by presenting them with exploded parts diagrams. You put them behind the wheel, show what happens when you do this or that. Then, in order to understand WHY the car behaves that way, you pore over parts diagrams and blueprints. Thermodynamics is the first part, statistical mechanics is the second part. Are you willing to set aside the idea of entropy as disorder, and critically look at and investigate other ideas? I will set my ideas aside and listen to any counter-argument you have. PAR (talk) 20:39, 8 November 2020 (UTC)


 * Actually I wasn't being sarcastic, that was poor wording and I'm sorry that it came off that way. Everyone in this discussion clearly has a deep understanding of entropy, but I believe that depth is making it hard to think of the reader's needs. I'm also sorry I'm coming off as rude...but patience is wearing thin as the discussion gets weedier and weedier.


 * So yes, I propose that the first sentence(s) of the article on Introduction to thermodynamic entropy be something like, "Here are some examples of thermodynamic entropy change"


 * Thanks. I would like others to weigh in on the idea of starting out the article without saying what entropy is. In my opinion, that's an imperative for any encyclopedia article, let alone an introductory one. If I had to boil down my grievance here, that'd be it, and there's a long history of me making that point.


 * Are you willing to set aside the idea of entropy as disorder, and critically look at and investigate other ideas?


 * Absolutely, and I'd very much like to see those ideas. The current wording followed John McCaskey's suggestion of starting with microstates, without invoking disorder, which you've argued against — while also satisfying the imperative that the article start by giving an idea of what entropy is. I thought it was a good compromise.


 * We clearly disagree on what "entropy is". This article is an introduction to THERMODYNAMIC entropy. Thermodynamic entropy is defined by Thermodynamics. That is what entropy is. The second law says entropy never decreases. This impacts our senses and instruments as irreversibility. So I think the introduction should provide easily understood examples of irreversibility. That is my argument. What is your counter argument? as I understand it, what are you saying is that "examples of irreversibility do not demonstrate what thermodynamic entropy is, the concept of disorder based in an intuitive sense of order does." Is that about right? PAR (talk) 05:05, 9 November 2020 (UTC)


 * It is useful to say that thermodynamic entropy is a quantity that indicates the irreversibility of so-called 'natural' thermodynamic processes, but it is also worth saying how or why it indicates it. For me, a thing is what it is, and not something else. A statement that it indicates irreversibility is not a statement or definition of what it is in itself, nor of what else it might indicate. Entropy is a function or variable of the state of a system in its own internal state of thermodynamic equilibrium, while irreversibility is a general property of processes.Chjoaygame (talk) 05:22, 9 November 2020 (UTC)


 * Thermodynamics does not experimentally define entropy, it experimentally defines a CHANGE in entropy, which is always non-negative, by the second law. The idea that it is a state function is provable from just that. The fact that entropy increases until equilibrium is attained is experimentally identical to the statement that a process is irreversible. Experimentally means quantified measurements of a phenomenon, but these may be experienced non-quantitatively as well, and these experiences, quantified or not, constitute the essence of thermodynamic entropy. It is what it IS. Spreading, disorder, measure of ignorance, these are all concepts that belong to the statistical mechanical EXPLANATION of entropy, starting with the assumptions of the atomic theory of matter, etc. PAR (talk) 13:02, 9 November 2020 (UTC)


 * Though the thermodynamic definition of entropy may, as Editor PAR says, not be fully defined experimentally, and though it may, as Editor PAR says, be "provable just from that", thermodynamic entropy is still defined as a state variable or function. It is not, however, defined for a body that does not obey the minus oneth law.


 * The fact that entropy increases until equilibrium is attained is experimentally identical to the statement that a process is irreversible. I think this sentence is unsatisfactory. Entropy changes in a process, but such a change is not something of which the progress can be continuously monitored, because entropy is not continuously defined during a thermodynamic process. Boltzmann's H function is not entropy, though its mathematical formula might suggest it. I have more objections to this sentence, but perhaps they are not needed right now.


 * Spreading, disorder, measure of ignorance, these are all concepts that belong to the statistical mechanical EXPLANATION of entropy, starting with the assumptions of the atomic theory of matter, etc. I would say not so much that the concepts are explanations of thermodynamic entropy as they are ordinary language interpretations of it. In general, an ordinary language interpretation is not a scientific explanation.Chjoaygame (talk) 13:38, 9 November 2020 (UTC)


 * Chjoaygame invoked "spread or dispersal." Could we start the article by saying that entropy is a measure of spread or dispersal? Just trying to get something rolling.  -Jord gette  [talk]  00:16, 9 November 2020 (UTC)


 * I object to that because that is not what thermodynamic entropy IS, it is a hypothetical explanation of it. Are you saying that "examples of irreversibility do not demonstrate what thermodynamic entropy is, the concept of disorder based in an intuitive sense of order does."? If so, come out and say it or whatever it is you mean. I've said what I mean. Point out where I am wrong and why, and why you are right, please. I will listen. PAR (talk) 13:02, 9 November 2020 (UTC)


 * I think that thermodynamic entropy is a state function or variable that can be experimentally determined, with respect to a suitably chosen set of reference states, by a suitable sequence of thermodynamic processes of which the crucial ones are transfers of energy as heat when the system is at defined temperatures, while transfers of energy as work, as well as matter transfers, are often also necessary ingredients in the determination. The formula of Clausius gives the precise values of entropy change for the respective sequential heat transfers. This definition of entropy makes no mention of irreversibility. Irreversibility is a further fact, not part of the definition of entropy, found by analysis of suitable sets of sequences of processes.Chjoaygame (talk) 13:56, 9 November 2020 (UTC)


 * PAR, I cannot believe that you still don't understand my point. To be clear, no, I am not saying we have to start with disorder, or with macrostates. I'm just saying we have to start with something, not nothing.


 * An encyclopedia article about a noun must begin with a direct description or definition of what that noun is. It cannot skip over the description or definition and begin with something else. Consider the following introductory articles and how they begin:


 * Introduction to general relativity General relativity is a theory of gravitation developed by Albert Einstein between 1907 and 1915.
 * Introduction to quantum mechanics Quantum mechanics is the science of very small things.
 * Introduction to evolution Evolution is the process of change in all forms of life over generations, and evolutionary biology is the study of how evolution occurs.
 * Introduction to electromagnetism Electromagnetism is one of the fundamental forces of nature.
 * Introduction to genetics Genetics is the study of genes and tries to explain what they are and how they work.


 * Do you glimpse a pattern there? Each of those articles begins by saying what the noun is, and I challenge you to find an article on any noun that doesn't. We cannot begin this article with "Here are some examples of thermodynamic entropy change." We cannot begin this article with "The idea of irreversibility is central to the understanding of entropy," which was how it stood one year ago (after the still-existing first sentence about it being an important concept in thermodynamics, which is fine). Please, I beg you to not make me have to explain this yet again, and I beg all of you to come up with a suitable first and second sentence, having rejected my suggestions and the present one suggested by John McCaskey.


 * Question for everyone — What is entropy? Please answer that question directly in the form of a sentence or two that can be understood by the lay reader, not a paragraph of abstractions.  -Jord gette  [talk]  18:26, 9 November 2020 (UTC)


 * Editor Jordgette is asking for something that he is not characterizing well. There are differences between various kinds of noun. Editor Jordgette is not dealing well with such differences.


 * A topic or general area of discourse is different from a specific concept within a general topic.


 * The nouns of Editor Jordgette's list — general relativity, quantum mechanics, electromagnnetism, genetics — refer to topics or areas of discourse, while entropy is a specific concept within a general topic.


 * In the case of entropy, it seems to me that Editor Jordgette is asking not for a definition, but rather for a general account or description. To me, he seems to be asking for some sentence such as 'In thermodynamics, entropy is a physical quantity that gives precision to the assertion of irreversibility of thermodynamic processes that is made by the second law of thermodynamics.' That sentence does not define entropy, but rather it gives a description of it.Chjoaygame (talk) 23:04, 9 November 2020 (UTC)


 * I would like one or the other. This is the closest we've gotten to a suitable and normal first sentence: Entropy is a physical quantity that gives precision to the assertion of irreversibility of thermodynamic processes that is made by the second law of thermodynamics. While I think that is not very layperson-friendly and can be improved, it's a start in the right direction. Others' thoughts?  -Jord gette  [talk]  01:26, 10 November 2020 (UTC)


 * I like Chjoaygame's sentence, and yes, maybe we could make it less technical sounding. Jordgette's pointed disagreement with the idea of beginning with a list of examples of entropy change is taken, I agree with that, good point. Chjoaygame's sentence addresses that problem while not confusing thermodynamic entropy with the statistical mechanical explanation. Could we then expand on Chjoaygame's sentence, clarifying it, by noting that thermodynamic entropy change is the thing that we experience and measure, and then using examples of realistic entropy change? And how this leads directly to the question "why does it behave that way?" which leads to Boltzmann and all the various takes on the link that he proposed between information entropy and thermodynamic entropy, without confusing the situation with a lot of technical stuff, just simple examples. Without even mentioning the term "informaton entropy" until later. PAR (talk) 02:33, 10 November 2020 (UTC)


 * Good! Great! Apologizing in advance for "dumbing down," what do you think of this version, which also draws on the suggestion below by Dirac66: In thermodynamics, entropy is a kind of number that points to the irreversibility (one-way direction) of natural processes. Irreversibility is asserted by an important law of nature known as the second law of thermodynamics, which says that in a system undergoing change, entropy never decreases and generally increases over time. Examples of thermodynamic irreversibility are the spread of heat from a hot body to a cold one, and the spread of cream after it is poured into a cup of coffee. And then maybe from there, the idea of watching a movie of these processes forwards vs. in reverse.  -Jord gette   [talk]  17:22, 10 November 2020 (UTC)


 * Ha. I don't think its "dumbed down" enough. With that lady's kids in mind, how about: In thermodynamics, entropy is a number that shows how physical processes can only go in one direction. For example, you can pour cream into coffee and mix it, but you cannot "unmix" it. You can burn a piece of wood, but you can't "unburn" it. If you watch a movie running backwards, you can see all sorts of things happening that are impossible. For the things that are possible, the number known as entropy always increases, when the coffee is mixed, when the wood is burned, or the movie is running forward. When the impossible things happen, entropy decreases. Another word for saying that things can only happen in one direction, is to say that the process is "irreversible". Irreversibility is described by an important law of nature known as the second law of thermodynamics, which says that in a system undergoing change, entropy never decreases and generally increases over time.


 * A few more random sentences:


 * In 1850, a scientist named Rudolph Clausius gave a very careful way of measuring entropy, and stated for the first time the second law of thermodynamics which says that in a system undergoing change, entropy never decreases and generally increases over time.


 * However, scientists are not content with simply measuring things and linking those measurements together with various laws. They prefer to not only understand how entropy behaves, but to also understand WHY it behaves the way it does. Twenty seven years later, in 1877, another famous scientist named Ludwig Boltzmann was very successful at answering that question. PAR (talk) 01:44, 11 November 2020 (UTC)

That's very good from a science-communication standpoint. Thanks. Unfortunately the discussion has fragmented, and now there's an editor in a new section objecting to focusing on irreversibility :-( It makes me wonder if this can ever be agreed upon with such a diversity of perspectives.  -Jord gette  [talk]  17:44, 11 November 2020 (UTC)


 * That editor practically rejects outright the thermodynamic approach, insisting instead on a highly mathematical statistical mechanical approach. I think we are agreed on taking the thermodynamic approach.Chjoaygame (talk) 18:30, 11 November 2020 (UTC)

new paragraph
For the sake of clarity in our joint work here, may I suggest the following terms?

The article has components

title - Introduction to thermodynamic entropy

lead - of about four or so paragraphs, with no section title; this is a summary of the article's body; the article's body must be thoroughly supplied with reliable sources, but it is not so for the lead summary; it is not an exposition of the theme of the article.

initial sentence or two of the first paragraph of the lead, conventionally including or wholly comprised of a brief general and often somewhat abstract definition of the topic of the article

remainder of lead

article section called 'Introduction'. This is optional. Some articles have one, others don't.

article sections with various titles, for their respective more detailed accounts of the topic.Chjoaygame (talk) 03:08, 9 November 2020 (UTC)

Some further comments

The underlying idea of entropy was invented around 1850, by Rankine, and some years later by Clausius. Rankine unimaginatively called it "the thermodynamic function". More imaginatively, Clausius called it "entropy", a word of his original invention.

There are some sober writers who point out that, before Rankine and Clausius, Carnot used two words, 'chaleur' and 'calorique'. They propose that calorique suggests entropy.

In the early days, it referred to processes affecting a 'closed' system; that is to say, transfer of matter was prohibited. Increase of entropy then described spread of energy as heat. Heat refers to energy entering or leaving the system, without regard to what happens in the surroundings.

Clausius used the ordinary language term 'disaggregation' to refer to such spread of energy. Later, transfer of matter was considered, for 'open systems'. Then spread of matter became relevant, but I am not aware of people speaking of it so.

Boltzmann used the term 'disorder' in a statistical or probabilistic conception of things, but did not seem to refer to something that makes purely macroscopic sense, such as spread.

In 1949, Guggenheim revived the Clausius idea of disaggregation, without actually citing Clausius. Guggenheim used the words 'spread' and 'dispersal', referring to spread in an abstract 'space' of microscopic states, perhaps as countable, as thermodynamic operations made more microscopic states 'accessible' to the system. This retained allusion to the ordinary language macroscopic notion of disaggregation.

Soon, Jaynes brought to bear in statistical mechanics a probability interpretation of Shannon's 1949 information theory. This changed the language but I think not the mathematical formulas of the topic.Chjoaygame (talk) 03:51, 9 November 2020 (UTC)

another new header 1
Perhaps the first paragraph of the lead might go


 * 'In thermodynamics, entropy is a numerical indicator of the irreversibility of natural processes. Examples of thermodynamic irreversibility are the spread of heat from a hot body to a cold one, and the spread of cream after it is poured into a cup of coffee.'

Then perhaps


 * 'Thermodynamic entropy is measured primarily through the ratio of quantity of heat to the temperature at which at which it enters a cold body. Because the cold body's temperature often increases as it is heated, a measurement of a large increase of entropy is best conducted gradually or in small steps, the hot body being kept just marginally hotter than the cold one.'

The third paragraph might start


 * 'Thermodynamic irreversibility is explained by the molecular composition of matter.'Chjoaygame (talk) 04:53, 10 November 2020 (UTC)


 * Re first paragraph: of course we have to warn the reader about over-generalizing and guessing the direction of a spontaneous process from its apparent increase in "disorder". Simple examples of apparent exceptions: heat can be transferred from a cold body to a hot one if enough work is provided, as in a heat pump or a refrigerator. And although cream will mix with coffee, oil will not mix with water. We can explain that the second law provides a quantitative criterion for deciding the real direction of each process under given conditions. Dirac66 (talk) 15:56, 10 November 2020 (UTC)


 * I don't see the above suggested first paragraph of the lead as explicitly proposing in general that one would guess the direction of a spontaneous process. I think most people know that heat spread from a cold body to a hot one does not occur, though they may not think of calling it a natural thermodynamic process. Energy transfer yes, as work, but so far, our exposition has not referred to work. Perhaps alongside talk of irreversibility, we should talk about work done by the surroundings appearing in the system as heat, as an example of creation of entropy. Rumford and Joule would like that, though neither of them had heard of entropy when they did their experiments.


 * To expound the second law in the first paragraph of the lead would take the topic of the article beyond entropy itself.


 * In am not in favour of placing in the first paragraph of the lead the proposed sentence "Irreversibility is asserted by an important law of nature known as the second law of thermodynamics, which says that in a system undergoing change, entropy never decreases and generally increases over time." Placed there, it spreads the topic of the article too far.


 * Moreover, the clause "entropy ... generally increases over time" is misleading, suggesting that in general the increase over time of entropy in a thermodynamic process can continuously monitor its course. One may wish that such were possible, and I think many feel that it is possible, but, sad to say, thermodynamics doesn't fulfil that wish. And I think we don't need to cater for readers who are so dumb that they don't know what 'indicator' means.


 * Perhaps some such sentence could appear in a third or fourth paragraph of the lead, depending on how the article develops.


 * Much as some would like to use a movie being played in reverse, such would, in general, not illustrate entropy or the second llaw of thermodynamics. Thermodynamics is about a specific kind of body and process, belonging to a closely defined logical 'universe of discourse', not about the universe or ordinary world at large as it would figure in many movies. Talk of the 'entropy of the universe' is found widely, as if thermodynamics applies to the ordinary world or universe at large. Sad to say, it doesn't, and we should not help spread such talk.Chjoaygame (talk) 18:45, 10 November 2020 (UTC)
 * The proposed first paragraph is factually correct, but the problem with this definition is that it turns the second law of thermodynamics into a tautology. The second law says that entropy always increases in an irreversible process. But by invoking reversibility, we're defining entropy as the measure of what always increases. Here's another attempt:


 * "Entropy is a foundational concept in the study of thermodynamics. Invented by Rudolf Clausius, entropy is traditionally defined as a numerical measure of disorder. Alternatively, many physicists believe it is better to think of entropy as a measure of energy dispersal at a particular temperature. The second law of thermodynamics says that entropy never decreases in a closed system, meaning entropy is also a measure of irreversibility."


 * That at least introduces the traditional/modern views in a way that's fair and not too complicated. &#12296; Forbes72 &#124; Talk &#12297; 20:05, 10 November 2020 (UTC)


 * Editor Forbes72 is here taking the sentence "In thermodynamics, entropy is a numerical indicator of the irreversibility of natural processes" as a definition of entropy. That is not how the sentence is intended. The intention of the sentence is to give an introductory description or characterization of entropy. A definition of entropy is hardly suitable in the first sentence of the article; it would be too complicated and would defeat the purpose of the article, to be an introduction. Editor Forbes72 offers a first sentence that is another description or characterization of entropy; that shows that he does not set much store on defining entropy in the first sentence. He then first offers what he calls a traditional definition, one that rejects the current plan to re-title the article 'Introduction to thermodynamic entropy'. Moreover, his offering is not a definition, but, rather, is an interpretation. True, his interpretation is widely recited, but it is not the interpretation that seems to have some current acceptance in this talk page discussion. The interpretation that he offers is practically meaningless in context, and, I guess, would baffle and confuse the newcomer. There is no one in the current mainstream that I know of who actually offers a defence of that widely recited interpretation; rather, it is simply recited like an incantation inherited by tradition. Editor Forbes proposes that the concept of entropy was invented by Clausius; it was invented first by Rankine, and, later, the name was invented by Clausius. Then Editor Forbes72 offers a second interpretation, the one that seems to have current acceptance in this talk page discussion. It is not likely to help the introductee to be exposed to two practically contradictory interpretations in the first paragraph of the lead. Then Editor Forbes72 offers a poorly constructed version of the second law, with a further interpretation in the same sentence. Editor Forbes72 offers as justification for his proposed wording that it is "fair and not too complicated". I do not favour Editor Forbes72's proposal.Chjoaygame (talk) 21:04, 10 November 2020 (UTC)
 * I'd love to define entropy in the first sentence. My proposal would be the traditional "entropy as disorder" is the most natural definition, but I moved it to the second sentence as a compromise since you seem to favor more recent points of view. I like the idea of changing the title to "Introduction to thermodynamic entropy" so I'm not sure why you think I reject it. You may not like the "entropy as disorder" but it's clearly the most widely given definition, from basic physics textbooks like
 * James S. Walker 2nd edition pp.592 "In this section we introduce a new quantity that is as fundamental to physics as energy or temperature. This quantity is referred to as entropy, and is related to the amount of disorder in a system"
 * Young and Friedman 13th edition pp. 669 "The second law of thermodynamics, as we have stated it, is not an equation or aquantitative relationship but rather a statement of impossibility. However, the second law can be stated as a quantitative relationship with the concept of entropy, the subject of this section. We have talked about several processes that proceed naturally in the direction of increasing disorder. Irreversible heat flow increases disorder because the molecules are initially sorted into hotter and cooler regions; this sorting is lost when the system comes to thermal equilibrium. Adding heat to a body increases its disorder because it increases average molecular speeds and therefore the randomness of molecular motion. Free expansion of a gas increases its disorder because the molecules have greater randomness of position after the expansion than before. Figure 20.17 shows another process in which disorder increases. Entropy provides a quantitative measure of disorder."
 * websites like HyperPhysics "the concept of entropy is that nature tends from order to disorder in isolated systems . ".
 * They don't offer a defense because it's the WP:MAINSTREAM interpretation. It's the alternative definitions that get argued for. &#12296; Forbes72 &#124; Talk &#12297; 21:40, 10 November 2020 (UTC)


 * Thank you, Editor Forbes72, for your thoughtful reply. It is a pity that it doesn't persuade me.


 * Some days ago I warned about the clout of diehards for the 'disorder' interpretation. Some months ago I made for myself a little survey of sources on the matter. The diehards have the numbers. I think participants here mostly agree that 'disorder' is not a part of the definition of entropy; no, it is an interpretation intended to give an intuitive feel for the concept, something quite different from a definition. A definition of entropy has to be in terms of a ratio of an energy quantity to a temperature. Clausius' word 'disaggregation' is older than the Boltzmann word 'disorder'. It is nearly synonymous with Guggenheim's 'spread' and 'dispersal'. The purpose of the article is to give the newcomer some introductory physical understanding. Amongst reliable sources who have actually considered the physics, as distinct from reciting the tradition, it is agreed that 'disorder' is verging on nonsense in the context. To escape favour of the diehard 'disorder' interpretation of the word 'entropy' over the helpful 'dispersal' interpretation, I favour exclusion of both, because inclusion of 'disorder' as an interpretation of 'entropy' would gravely impair the effectiveness of the article, in its intention to be an introduction helpful towards physical understanding. Inclusion of 'disorder' as an interpretation of 'entropy' would encourage parrot-like recital as opposed to physical understanding. I concede that your quote from Young and Friedman is an attempt at defence of the use of the word 'disorder', a defence that I had not read. The defence to me reads more as shoehorning than as clarification. I don't find it nearly as helpful as the 'spread' interpretation.


 * The reason why I think you reject the topic as thermodynamic is that 'disorder', which you prefer, and indeed propose as a "definition", is not a thermodynamic concept. It is a molecular statistical mechanical concept, quite foreign to thermodynamics proper, which is a macroscopic theory. To base the article on 'disorder' would be erase a thermodynamic approach. Perhaps this view seems strange to a generation that most regrettably has been taught to confound thermodynamics with statistical mechanics, to the stage that practically erases thermodynamics as a subject in itself. For thermodynamics proper, the interesting topics are such as the Legendre transform connection of the conjugate extensive and intensive variable pairs.


 * In the proposed first paragraph
 * 'In thermodynamics, entropy is a numerical indicator of the irreversibility of natural processes. Examples of thermodynamic irreversibility are the spread of heat from a hot body to a cold one, and the spread of cream after it is poured into a cup of coffee.'
 * the use of the word 'spread' is deliberately avoided as an explicit interpretation of the concept of entropy. Instead, in that proposal, the word 'spread' is used as a description of processes themselves. I think it is natural. The word 'disorder' would not fit there.Chjoaygame (talk) 23:32, 10 November 2020 (UTC)
 * I should clarify. I am advocating to display the disorder explanation prominently because it's prominent in the literature. I am not personally endorsing the disorder explanation. It definitely takes some explanation to justify why a packet of salt and a glass of water separately can be thought to be more "ordered" than a glass of salt water. So there very well could be a more straightforward intuitive picture. But that's just my opinion. Even if everyone on this page was a verified subject matter expert, Wikipedia is not the appropriate forum to tell physics textbook authors that "hey, actually most of you all have been explaining the concept the wrong way". The idea of entropy as disorder is pretty deeply embedded - and not just in the introductory texts. Pathria and Beale, 3rd edition pp. 5 has: "Now, in the study of the second law of thermodynamics we are told the increase of entropy is related to energy content of the universe, in its natural course, is becoming less and less available for conversion into work; accordingly, the entropy of a given system may be regarded as a measure of the so-called disorder or chaos prevailing in the system." Granted, this talk page shows significant dissent from the "entropy as disorder" idea, and citations in scientific literature to back it up. However, in terms of due weight, I think "entropy as irreversibility" qualifies as a view held by a significant minority. Lively debate on the merits of the subject is great for a journal publication, but (99% of the time) the appropriate thing on Wikipedia is ignoring one's personal opinion and just summarizing what the majority of the expert literature says. &#12296; Forbes72 &#124; Talk &#12297; 03:58, 11 November 2020 (UTC)


 * Thank you, Editor Forbes72, for your helpful clarification. I am comforted by it.


 * For myself, I do not like to say just that entropy is irreversibility. I think that wording is semantically indefensible. It has at most only one proponent here, and even then it is not said exactly so; Editor PAR wrote something different: "The essence of entropy is irreversibility". A direct statement that entropy is irreversibility has no explicit support in the literature. The reliably literature-supported counter to 'disorder' is 'dispersal'. Yes, we all agree that entropy is an indicator of irreversibility, but entropy is not itself irreversibility. To say that entropy is an indicator of irreversibility is not to say that entropy is irreversibility.


 * To be perhaps over pedantic, as I parse the sentence in your quote from Pathria and Beale, it is ungrammatical. But more substantially, they use the words "we are told" and "so-called". I think that lets the cat out of the bag. They themselves see that the 'disorder' interpretation verges on nonsense; they see themselves as appeasing the diehards. They can't fairly be cited as a reliable source that explicitly supports it with a clear defence.


 * Indeed, I think it perfectly reasonable to say, alongside the statement that entropy is an indicator of irrreversibility, that it is also an indicator of the unavailability of intrinsic energy for thermodynamic work. I use the slightly unorthodox term 'intrinsic energy' here for the sake of including the various system energy functions or variables such as internal energy, enthalpy, Helmholtz free energy, and so on. Thermodynamic work is conveniently distinguished from such work as the lifting of a weight in the surroundings. Then one can comfortably say such things as 'thermodynamic work is available to be harnessed to do the work of lifting a weight in the surroundings'.


 * As for the interpretations as 'disorder' and 'dispersal', I will hold to what I wrote above, which I have now put into magenta font for easy reference. That way we can improve the article and avoid futile editorial conflict that I think would damage Wikipedia. If pressed, I am inclined to say that anyone who seriously supports the disorder interpretation is not a reliable expert on the topic, relative to the weighty reliability of Guggenheim, Jaynes, Denbigh, Atkins, and Grandy. I am unhappy with saying that 'disorder' is an explanation; I prefer to say that it is an interpretation. We can avoid such confusing interpretation by not mentioning it.Chjoaygame (talk) 07:09, 11 November 2020 (UTC)

another new header 2
Perhaps the first paragraph of the lead might go


 * 'In thermodynamics, entropy is a numerical indicator of the irreversibility of natural processes. Examples of thermodynamic irreversibility are the spread of heat from a hot body to a cold one, and the spread of cream after it is poured into a cup of coffee. Entropy is also a quantitative guide to the unavailability, due to inevitable natural inefficiency, of the intrinsic energy of a body of matter or radiation, for thermodynamic work that can be harnessed to do mechanical work outside the body. A traditional example is found in the operation of a steam engine. Thermodynamic irreversibility and natural inefficiency are like the two sides of the same coin. This was gradually brought to light, starting with the writings of French engineer Sadi Carnot.'

Then perhaps the second paragraph.


 * 'Thermodynamic entropy is measured primarily through the ratio of quantity of heat to the temperature at which at which it enters a cold body. Because the cold body's temperature often increases as it is heated, a measurement of a large increase of entropy is best conducted gradually or in small steps, the hot body being kept just marginally hotter than the cold one.'

The third paragraph might start


 * 'The measured values of entropy are explained by the molecular composition of matter and the photonic composition of light. For some forms of matter and light, the measured values are even theoretically predictable through that explanation.'

Just some proposals.Chjoaygame (talk) 13:30, 11 November 2020 (UTC)


 * I think these paragraphs contain too much jargon, that is, words that are not understood by the new reader amd need to be introduced. "Irreversibility", "intrinsic energy", "mechanical work", "natural inefficiency" are examples. These are, however, good words for the Entropy (thermodynamics) article. In this introductory article, I think we need to:


 * 1) Relate a change in entropy to our senses which, when quantified, constitutes a measurement, and demonstrate how there is a particular direction to everyday processes. Define irreversibility.


 * 2) State that the measurement process defines the change in thermodynamic entropy, and how the second law describes its behavior (non-decreasing)


 * 3) Explain that there is something lacking - Thermodynamics defines and describes how entropy behaves, but does not explain WHY it behaves the way it does.


 * 4) Introduce Boltzmann and his explanation of the above. HERE is where we introduce the atomic theory of matter, macrostate, microstate, "Ways", etc. etc.


 * 5) Describe various "takes" on entropy, mixing, disorder, lack of information, etc.


 * To this end, I will restate some suggestions I offered to Jordgette:


 * In thermodynamics, entropy is a number that shows how physical processes can only go in one direction. For example, you can pour cream into coffee and mix it, but you cannot "unmix" it. You can burn a piece of wood, but you can't "unburn" it. If you watch a movie running backwards, you can see all sorts of things happening that are impossible. For the things that are possible, the number known as entropy always increases, when the coffee is mixed, when the wood is burned, or the movie is running forward. When the impossible things happen, entropy decreases. Another word for saying that things can only happen in one direction, is to say that the process is "irreversible". Irreversibility is described by an important law of nature known as the second law of thermodynamics, which says that in a system undergoing change, entropy never decreases and generally increases over time.


 * A few more random sentences:


 * In 1850, a scientist named Rudolph Clausius gave a very careful way of measuring entropy, and stated for the first time the second law of thermodynamics which says that in a system undergoing change, entropy never decreases and generally increases over time.


 * However, scientists are not content with simply measuring things and linking those measurements together with various laws. They prefer to not only understand how entropy behaves, but to also understand WHY it behaves the way it does. Twenty seven years later, in 1877, another famous scientist named Ludwig Boltzmann was very successful at answering that question.PAR (talk) 05:37, 13 November 2020 (UTC)

commentary
For ease of editing, I have copied and re-coloured the above. I have also removed Editor PAR's signature. The new colour intends to indicate the authorship.

Forgive me, I am about to say things that will likely be unwelcome. The more I think about this, the less sanguine I feel about it. There are good reasons why in the past, thermodynamics was not taught till university or perhaps college. I don't know the practice today. There are good reasons why science uses terms of art. They are not just obscurantist rewrites of ordinary language. The following comment is pertinent: "It seems to me it boils down to "Let's not think about it" for "teaching purposes" (pedagogy)." Pedogogy should not be used as an excuse for sloppy talk or for sloppy thinking, or for making statements that are not based on reliable sources.

I think that the project of a super-simplified treatment of entropy in context of the second law of thermodynamics is at least heroic and best precarious. The topic is notorious for its great difficulty. Peter Atkins' book title Four Laws that Drive the Universe lets the cat out of the bag. It is a recklessly grandiose boast. In my opinion, we have little or no reliably reportable idea of the overall evolution of the universe. Is the ordinary physical world finite? What would it mean to say that it's not? I don't need to ask further questions along those lines, for I guess Editors have their own such questions. Atkins must be a god-professor at least, to indulge himself in such vanity. In his favour, he supports the 'spread' interpretation, but that doesn't justify his hubristic claim. Let's not pursue such lines of thought.

As I have written above, the existence of this article is an invitation to unbridled editorial opiniation. We should not license that. We should bear in mind how Wikipedia editing works. Gresham's law of currency comes to mind: "Bad currency drives out good." People will hold onto a silver dollar that slips into their hands, not give it to the grocer; they will give the grocer a bad coin that someone has given them.

Though our present company of Editors may have exceptional genius, we should bear in mind that other Editors, probably less talented, will soon take over the article with a diversity of wonderful 'improvements'. The mind boggles.


 * In thermodynamics, entropy is a number that shows how physical processes can only go in one direction. For example, you can pour cream into coffee and mix it, but you cannot "unmix" it. You can burn a piece of wood, but you can't "unburn" it. If you watch a movie running backwards, you can see all sorts of things happening that are impossible. For the things that are possible, the number known as entropy always increases, when the coffee is mixed, when the wood is burned, or the movie is running forward. When the impossible things happen, entropy decreases. Another word for saying that things can only happen in one direction, is to say that the process is "irreversible". Irreversibility is described by an important law of nature known as the second law of thermodynamics, which says that in a system undergoing change, entropy never decreases and generally increases over time.

"Entropy is a numerical indicator" is marginal, but entropy is a number goes over the line. Entropy is a physical quantity, with a dimension.

It is bad enough that there are some more or less professional physicists who seem to believe that the second law of thermodynamics applies to processes that do not lie within the purview of thermodynamics. I think such beliefs lie between wild claims and delusions of grandeur. Clausius talked about "the universe". I think his pronunciamentos were better confined to 'the thermodynamic universe of discourse'. When it comes to distinguishing work and heat, it can be done properly in thermodynamics, but not in a general physical universe. Hiding this is a first step of brainwashing children into parrotism.

To say that physical processes can only go in one direction is at first sight mystifying. What is the direction of a physical process? North, south, east, west, up, down, to the left, clockwise? It is not required of a thermodynamic process that it occur along a unique path, so the question of 'direction' is not just about time. It verges on the classic question from the teacher to the pupil: 'guess what I'm thinking!' The sentence as currently written relies on progress being conceived as just going forwards or backwards in time. Someone who can't be assumed to know the meaning of the words 'indicator' and 'irreversible' can't be assumed to have an intuition for backwards running time. Even playing a movie backwards is questionable for such a person.

I also object to things can only happen in one direction.. In logic, "things" belong to their respective universes of discourse. Non-trivial thermodynamic processes can run in only one direction. This may be hard to express for children, but that is a challenge for pedagogy, not an excuse for sloppiness. A piece of wood is perhaps nearly a thermodynamic system. But the events in a general movie go too far from thermodynamics. To pretend or tacitly imply that they don't is reprehensible. For the things one sees in movies, entropy is mostly undefined. To pretend or tacitly imply that it is defined is reprehensible. Such pretences or innuendos start the reader on a road of delusion of grandeur or parrotism, or of merely incurably loose thinking. The motion of a planet in its orbit is not a thermodynamic process.

When the impossible things happen ... Impossible things don't happen.


 * A few more random sentences:


 * In 1850, a scientist named Rudolph Clausius gave a very careful way of measuring entropy, and stated for the first time the second law of thermodynamics which says that in a system undergoing change, entropy never decreases and generally increases over time.

That is not accurate history. Clausius didn't get it clear till 1865. It is also not accurate physics. The second law of thermodynamics is not a law of general physical processes. It is a law of thermodynamics.

a system is high jargon. The traditional term is 'body'.


 * However, scientists are not content with simply measuring things and linking those measurements together with various laws. They prefer to not only understand how entropy behaves, but to also understand WHY it behaves the way it does. Twenty seven years later, in 1877, another famous scientist named Ludwig Boltzmann was very successful at answering that question.

I am not keen on telling children foremost about the degree of successfulness that Boltzmann achieved.Chjoaygame (talk) 07:22, 13 November 2020 (UTC)


 * Let me attempt another version based on the above objections:


 * In thermodynamics, entropy is a numerical quantity (like a measurement) that shows that all but the simplest physical processes can go in only one direction. For example, you can pour cream into coffee and mix it, but you cannot "unmix" it; you can burn a piece of wood, but you can't "unburn" it. If you reversed a movie of coffee being mixed or wood being burned, you would see things that are impossible in the real world. Another way of saying that those reverse processes are impossible is to say that mixing coffee and burning wood are "irreversible". Irreversibility is described by an important law of nature known as the second law of thermodynamics, which says that in a system undergoing change, entropy never decreases and generally increases over time.  -Jord gette  [talk]  19:21, 13 November 2020 (UTC)


 * I take the just foregoing "another version" as a proposal for the first paragraph of the lead of the article Introduction to thermodynamic entropy. I think it doesn't comply with the ordinary form of such paragraphs in Wikipedia, and doesn't improve on that form. Its content is more suited to the body of the article. It tries to elaborate the meanings of the words 'entropy' and 'irreversible' and to state the second law of thermodynamics, all in a short paragraph. Editor Jordgette wants to compress a university course (one that presupposes several years of physics study) into a few sentences, all pre-digested for a child who hasn't studied physics. In a Wikipedia lead paragraph, a few examples may be mentioned, but only barely, and should not be elaborated. The comments that I offered were intended to warn off, not to propose elaboration.Chjoaygame (talk) 23:17, 13 November 2020 (UTC)


 * Editor Jordgette wants to compress a university course (one that presupposes several years of physics study) into a few sentences, all pre-digested for a child who hasn't studied physics


 * Yes, indeed that is what the lead paragraph to a Wikipedia article titled Introduction to thermodynamic entropy should do. I am trying to move this article along, there already being some 400 million words on this page on what entropy is and is not, in the opinion of a variety of knowledgable (though long-winded) editors. The proposed paragraph is an edit of a proposal by editor PAR, incorporating your suggestions. Please understand my desire to find consensus on the lead paragraph.


 * How would you write the paragraph, keeping in mind this is Introduction to thermodynamic entropy? Or, perhaps do you think this article should not exist? Deletion has been proposed previously (above) and sadly this seems to be an increasingly viable option, since consensus is not being reached here, even on a first sentence. It may be an inappropriate topic for an introductory article.  -Jord gette  [talk]  00:28, 14 November 2020 (UTC)


 * Very often, the lead of a Wikipedia article has several paragraphs. I think the lead of this article should have several paragraphs. The lead should summarise the article. It should not try to compress the topic into a few sentences. In particular, it is bad form to elaborate examples in the first paragraph of the lead. I think Editor PAR went off beam by proposing such. Elaboration of examples belongs in the body of the article. Summary is not the same as compression; the difference matters. Besides the first paragraph of the lead, there are many more parts of the article to consider. The lead includes further paragraphs. The body of the article is important. So far, all this seems to suffer neglect. Remember, the first sentence is an element of a summary. It is a good idea to see what is to be summarised before trying to summarise it.


 * If a person doesn't know the meaning of words such as 'indicator' and 'irreversible', he can't be expected to know what is meant by "all but the simplest physical processes." I have to admit that I don't know what it means.Chjoaygame (talk) 01:36, 14 November 2020 (UTC)

I like Chjoaygame's introduction, does anyone not? PAR (talk) 05:49, 14 November 2020 (UTC)


 * Thank you, Editor PAR. In direct answer to your question, I have my several doubts. One is in the marginal character of the phrase 'numerical indicator'; would 'quantitative indicator' be acceptable? I think we need to see a fair sample of the rest of the article in order to summarize it.


 * I continue to feel uncomfortable about the existence of this article. To me it seems ominously exceptional amongst Wikipedia articles. Can you very kindly point to other such articles? To me, this one seems to set a precedent for a radical and dangerous departure, from the usual run of Wikipedia articles, from modestly encyclopaedic to unduly pedagogic.Chjoaygame (talk) 07:38, 14 November 2020 (UTC)


 * PAR, which introduction are you referring to? The RfC has become so bloated I admit to having no idea who has proposed what, when. If you're referring to the one with the sentence Entropy is also a quantitative guide to the unavailability, due to inevitable natural inefficiency, of the intrinsic energy of a body of matter or radiation, for thermodynamic work that can be harnessed to do mechanical work outside the body, no, this is absolutely inappropriate for an introductory article and marginally appropriate for a standard article on thermodynamic entropy. If people don't know what an indicator is, they certainly will not know what "quantitative" or "intrinsic energy of a body" or "thermodynamic work" are.


 * I will state again my suspicion, based on how this RfC has played out, that the topic is inappropriate for an introductory treatment and that the article may need to be deleted. It seems Chjoaygame is also moving in this direction.  -Jord gette  [talk]  18:12, 14 November 2020 (UTC)


 * Can anyone very kindly point out other introductory articles in Wikipedia that achieve the level of apprehensibility, to a child or to another kind of reader, of a topic of a level of difficulty such as that of the nature of entropy?


 * I have looked, and found a perhaps comparable article, Introduction to general relativity. The first paragraph of its lead reads


 * General relativity is a theory of gravitation developed by Albert Einstein between 1907 and 1915. The theory of general relativity says that the observed gravitational effect between masses results from their warping of spacetime.


 * Is that comparable with our project?Chjoaygame (talk) 20:53, 14 November 2020 (UTC)


 * Yes, and on 9 November above I listed five such articles, Introduction to GR being one of them, along with their leading sentences. And we discussed them. But I think you will agree that introducing thermodynamic entropy is a far tougher nut to crack than what is accomplished in the five articles listed.


 * And, as you pointed out in that discussion, the other article titles "refer to topics or areas of discourse, while entropy is a specific concept within a general topic". I could not find any comparable "Introduction to" articles on specific concepts within general areas of discourse; they are all standalone areas of discourse. I suppose Introduction to viruses is a topic within the arena of biology, but the topic of viruses within biology is nowhere near as abstruse as the topic of entropy within thermodynamics. So, perhaps that is another strike against the existence of this article.  -Jord gette  [talk]  00:03, 15 November 2020 (UTC)


 * We have two obstacles. One is the intrinsic difficulty of the topic. The other is the desire to make the article apprehensible to a child who knows no physics. If we liked, we could drop that desire.Chjoaygame (talk) 01:01, 15 November 2020 (UTC)


 * This is not about a child or children. The vast majority of Wikipedia users are adults who are not trained in physics and, sadly, most are quite ignorant in science in general. Someone may have heard the word "entropy" in a casual conversation, gone to Wikipedia, found the main article far too technical, and clicked on the link for this nontechnical article. This article should be written for that person — not necessarily for a child. I am sorry but "a quantitative guide to the unavailability, due to inevitable natural inefficiency, of the intrinsic energy of a body of matter or radiation, for thermodynamic work" is not appropriate for such an audience.  -Jord gette  [talk]  01:26, 15 November 2020 (UTC)


 * Thank you for your helpful comment. For me, it makes significant progress, if it is agreed upon here.


 * From above


 * In an *introductory* article on acceleration, you would want to begin as if you were talking to a reasonably intelligent 12 year old, who is not yet mathematically sophisticated.


 * And


 * Please try to word the entry so that someone who doesn't understand physics at all, or at least only the very basics of physics--like high school physics, or even better, middle schoolphysics--can understand it. If that isn't possible, try to make a clearer path of the necessary research that needs to be done to understand it.


 * I am saddened to look on as this site becomes so useless to me and my youngsters that I no longer direct them here for any meaningful information in the sciences.


 * And


 * Editor Jordgette wants to compress a university course (one that presupposes several years of physics study) into a few sentences, all pre-digested for a child who hasn't studied physics.


 * Yes, indeed that is what the lead paragraph to a Wikipedia article titled Introduction to thermodynamic entropy should do.


 * And


 * With that lady's kids in mind, ...


 * Is it agreed that the article is for adults? I would regard such an agreement as marking significant progress here.


 * Moving to a more risky proposition. I think it off-beam to try to give an understanding of thermodynamic entropy to someone with no knowledge of physics. Disregarding a person who is motivated by no more than a desire to give an impression of educatedness, would someone with no knowledge of physics seriously want such an understanding? An understanding of the second law is much easier than an understanding of thermodynamic entropy. Carnot 1820, Rankine 1850, Clausius 1864. Many statements of the second law do not mention entropy. Should the title of the article be Introduction to the second law of thermodynamics?Chjoaygame (talk) 04:25, 15 November 2020 (UTC)


 * Is it agreed that the article is for adults? Yes and no. When I was ten years old, being interested in and knowledgable about science but not academically trained, I could have benefitted from this article. A 50-year-old executive with an MBA can similarly benefit from this article. I am motivated by this comment above: "Please make the introduction simpler. Think of it like this; I am a random person who has heard the word 'entropy' in a conversation. Now I want to look it up and find out what it means." That's pretty straightforward, isn't it? I assume everyone here is capable of imagining being such a person, and what kind of introduction would be helpful to them.


 * Disregarding a person who is motivated by no more than a desire to give an impression of educatedness Why disregard such a person? That is an elitist position — that if a person wishes to gain any insight into the word entropy, they must take a thermodynamics course with all of the prerequisites; otherwise they must not utter the word. Physicists don't get to decide that. As it stands, "entropy" can be found in many non-physics contexts. Consider this silly general-audience article, "Entropy, Politics and the Science of Love." It includes a painful attempt at describing entropy for the general audience. I hope we can do better.


 * Personally, if I were working on this article by myself, I would try to meet the lay reader's needs by giving an extremely informal description of entropy (not thermodynamic entropy, just entropy) that invokes order and disorder and perhaps irreversibility and the statistical mechanics explanation, and leave it at that. But I get that this is unacceptable to physicist–editors, and that's okay. The question remains whether we can satisfy both the lay reader who seeks a broad and informal understanding of the word and physicist–editors.


 * I think it off-beam to try to give an understanding of thermodynamic entropy to someone with no knowledge of physics. Then perhaps the article should not exist. That can be discussed in a future AfD if it comes to that.


 * Should the title of the article be Introduction to the second law of thermodynamics? I don't think so. "Entropy" is in far greater use in non-physics contexts than the 2nd law.  -Jord gette  [talk]  17:41, 15 November 2020 (UTC)


 * Ok.Chjoaygame (talk) 18:03, 15 November 2020 (UTC)

Rando commentary about above RfC
In the current version of this article, as of right now, I like the second paragraph, that talks about billiard balls. It's technically accurate. The first paragraph, mentioning cattle, is not. Talking about irreversibility is ... inappropriate and technically incorrect. Yes, in physics they do get tied together, but the reasons for this are subtle and arcane, having to do with the spectra of many-body Hamiltonian operators. Even most practicing physicists don't understand where irreversibility comes from; to start yammering about that in an "intro to" article is just ... trouble. In the strict mathematical sense, irreversibility has nothing at all to do with entropy, in any way shape or form. Zero, zippo, zilch.

When people say "irreversibility", they usually are thinking either of ergodicity or of mixing (mathematics), which is a kind of "2-ergodicity". If you are having trouble organizing your thoughts, you might want to read the "informal explanation" part of ergodicity. It mentions entropy a few times, it mentions irreversibility never. ... this is because "irreversibility" is not a necessary ingredient. ... its irrelevant. Also ... entropy is not "really" about order and disorder, although that is a common but deeply flawed explanation. Its got ... kind of little or nothing to to with disorder, per se, it is just that ... historically, the earliest examples of entropy looked like they were very disordered and random. And so this was assumed to be a property, and spread into popular lay-mans explanations. It's deeply flawed, because you then look at a living thing, a tree, an animal, or heck, a winding river or coastline, and start thinking of high order and "anti-entropy" which are the first footsteps towards ... nonsense and balderdash. The second paragraph, about the billiard balls, and the size of the configuration space, that's hitting the nail on the head. The entropy is the logarithm of that size; that is literally the strict technical definition of entropy. Refine that idea with more examples, and increasing sophistication. 67.198.37.16 (talk) 07:14, 11 November 2020 (UTC)


 * Thank you, Editor 67.198.37.16 for your comment. I would feel more comfortable chatting with you if you were very kindly to give youself an ordinary user name. I suggest you preserve your privacy by choosing a user name that hides your personal identity. If you do that, then, so far as I have found, it is secure to contribute to Wikipedia.


 * I am glad to read your admirable and clear rejection of the 'disorder' interpretation. I would comment that the earliest interpretation, that of Clausius, did not refer to disorder. Clausius was a thermodynamicist. He referred to 'disaggregation'. The 'disorder' interpretation came later, from Boltzmann, a statistical mechanic. This article seems to be headed to taking a primarily thermodynamic approach, with statistical mechanics secondary. I am proposing avoidance of explicit interpretation of entropy in the article in order to prevent futile editorial conflict between the 'disorder' and the 'dispersal' interpretations.


 * For the current proposals here in this discussion, talk of billiard balls, a statistical mechanical line, is secondary to the primary approach, which is thermodynamic as opposed to statistical mechanical. The discussion here recognises three chief usages of the word 'entropy', in thermodynamics where it originated, in statistical mechanics, and in informatics.


 * For the statistical mechanical account, you use the words 'size of the configuration space'. I like that. It is practically synonymous with the 'spread' or 'dispersal' interpretation.


 * Let us not forget the wisdom of the immortal Vladimir Igorevich Arnol'd, who wrote (from my faulty memory) "Every mathematician knows that it is impossible to understand an elementary course in thermodynamics." Thermodynamics is a topic in physics, not mathematics, and in physics it is usually taught poorly. For a generation, there was a regrettable educational fashion, of merging thermodynamics with statistical mechanics. That was a bad move. It left students with little understanding of thermodynamics per se.Chjoaygame (talk) 08:26, 11 November 2020 (UTC)


 * In the strict mathematical sense, irreversibility has nothing at all to do with INFORMATION entropy, in any way shape or form. Zero, zippo, zilch. The point is that this article is about THERMODYNAMIC entropy. Your mention of "the spectra of many-body Hamiltonian operators" firmly puts your word "entropy" into the statistical mechanical concept of entropy, which is the application of information theory to a "constructed" (rather than measured) physical system, with all the relevant assumptions, which is treated statistically, rather than as a determinate system.


 * I fully agree with your second paragraph regarding "disorder". I disagree that any mention of "configuration space" has anything to do with thermodynamic entropy, and has everything to do with the statistical mechanical explanation of thermodynamic entropy. PAR (talk) 05:50, 13 November 2020 (UTC)


 * Irreversibility is a sound physical and thermodynamic concept, whether explained or understood or not. It should be given prominence in this article. When many people think of physical irreversibility, I believe that ergodicity or mixing (mathematics) are not in their minds, but they are still thinking soundly. Their thinking is about an important but fundamentally non-mathematical topic, macroscopic physics, not even nearly about the spectra of many-body Hamiltonian operators. Those admirable but strictly mathematical concepts belong to a level of mathematical sophistication that even some mathematicians have not engaged with. They are not primary for this article as it is currently proposed.Chjoaygame (talk) 08:26, 11 November 2020 (UTC)


 * One is certainly entitled to believe whatever one wants, but beliefs should not be codified into wikipedia articles. Some 50 or 70 years have elapsed since Kolmogorov was working; many new things have been discovered and results obtained. It was pretty dramatic during the 1990's and 2000's, when lots of strong and sharp results were obtained. A historical account of CLausius and Kolmogorov's thinking is worthy, but it would be crazy to ignore research from the last 20-30 years.


 * As to volume: the entropy of the Bernoulli process is log 2. Period. End of story. Why? Because the volume of the coin flip is two: heads, tails, that's it. Let's try the billiard table, with 15 balls. Let's thermalize it so that the velocity of the balls follow some distribution, - Boltzmann, Maxwell, I don't care. Some crazy distribution invented by Joe Schmo on a weekend. What's the volume of that? Well, for each ball, its the size of the pool table, times the size of the distribution of velocities. Call that A. For N=15 balls, the volume is A^N. You can make N be avogadros number, don't care. The entropy is the log of that. The entropy is S= N log A. What's log A? Well, the balls occupy all positions uniformly, so that's a constant. What about the log of the velocity distribution? Well, that's an integral. Typically, you slice it up into equal volumes of delta-E E the energy, and look at how many balls have that energy. Then sum that up. The log of that integral is the entropy. Why are you choosing the energy as the unit of volume? Because the kinetic energy is (OK, here it gets complicated) the geodesics on a Riemannian manifold are given by the solution to Hamilton's equations of the Hamiltonian on the cotangent bundle which is H=p^2/2m where m is not the mass, but the inverse of the metric tensor and p is the momentum in canonical coordinates on the cotangent bundle (which is a symplectic manifold) That is why you use the energy to obtain the equal-volume slices when integrating over the invariant measure of the probability distribution. Because the geodesics describe the geodesic flow of the billiard balls, aka, the ergodic flow of the billiards. That is how you obtain the entropy for billiards. That's it, end of story. Nothing about disorder, in here. Nothing about irrerversibility. Just flows and geodesics and Hamiltons equations and invariant measures.


 * This is not a secret. The other day, I was reading some biology paper, where they were looking at the immunoglobulin for zebrafish (because zebrafish grow great in lab tanks!?) and have a small simple immune system (about 15 amino acids in the antigen binding sites). They wanted to model the genetic sequences, and the resulting proteins that show up in the highly-variable parts of the Ig and understand their 3D shapes. The very first thing they do is to compute the entropy of the system, using exactly the formulas I threw at you, up above. They then compare that to the entropy from protein folding models, the entropy of some electromagnetic model, and the entropy of the Ising model. What Ising model, you ask? Well, for each different amino acid in the variable ends of the Ig, it has a different affinity for the corresponding amino acid of the antigen it is detecting. This is a matrix, a Markov matrix, and the grand total energy is described by the Ising model of pair-wise interactions of the amino acids (related to the resonant recognition model oops redlink.) Dividing the energy into equal sized bins, taking the log, and integrating, gives you the entropy. Its the logarithm of the grand-total volume of the phase space you are working in (subject to the invariant measure, sliced into equal-sized bins by the energy) For zebrafish Ig, the phase space is the number of amino acids, weighted by affinities, to the power of the length of the antigen binding sites. They explicitly wrote down the equations for each of these things. Modelled it all on computer. Did the typically-colorful graphs that biologists love to do. Even biologists know how to correctly compute the entropy, as the log of the phase-space volume, these days.


 * So the above is about the entropy of some graph, picked out from zebrafish. What about the entropy of some graph, in general? Well, you can't know that until you know the weights of the edges on the graph, the transition probabilities. To keep it easy, do a neural net. Well, for the neural net, you need to identify the state transitions, and count how many of them there are, and weight each one. It's easiest to do this for something Markovian, because then you have a rather obvious expression telling you what parts of the graph are connected, and what the allowed state transitions are. Count the grand total number of states. That's your volume. Take the log. That's your entropy. Done. Period. End of story. No jibber jabber about order/disorder, although clearly, neural nets look very "disordered". Nothing about "irreversibility"; other than perhaps, while you are training the net, once it has set out on a particular learning path, it will remain "stuck" on that path, so in that sense it is "irreversible". But the entropy is path-independent -- it does not matter what training algo you used for that network, how long it took to train. The entropy depends ONLY on the number of neurons, and the probability of the size distribution of the weights. And specifically, the log of that. That's it. I think these three basic examples are straight-forward enough that you could walk through the toy-model calculations to get each of them.


 * What about irreversibility? Well, every invariant measure is the eigenvector of the largest eigenvalue given by the Frobenius-Perron theorem. For thermodynamic systems, it is always one, as otherwise, the measure would not be invariant. What about the other eigenvalues of the Frobenius-Perron operator? Well, they are either unitary, in which case you have a quantum system that is evolving unitarily, or they are less than one, in which case, those modes describe the decaying, transient states of the system. Those decaying modes are the dissipative part of the spectrum, that thing that you are calling "irreversibility". There is a famous theorem about irreversibility, its called the ergodic decomposition theorem Red link whoops. From the spectral point of view, its just saying that the eigenvalue-one part is the thermodynamic limit, and the eigenvalue less-than-one are the irreversible, decaying bits. That they decayed, and wandered away, (wandering set) that is what made it irreversible. They flowed downhill, and cannot come back up again.  After removing what can flow away, what is left is the volume of the space that you take the log of, to get the entropy.  So sure, there is an irreversible flow (see Katok's books, for example) but once you remove the flow, the system is static, and the log ov the volume of that system is the entropy. End of story.


 * Clausius didn't know this, but Kolmogorov did. Ornstein did, and apparently, even biologists get the gist of it, these days. The goal of this article should be to make this "common knowledge" rather than keeping it some obscure factoid known only to the initiated few. 67.198.37.16 (talk) 19:36, 11 November 2020 (UTC)


 * p.s. Arnold was right; my sophomore-college course in intro-to-thermodynamics was utterly befuddling. Which is maybe why I know so much about it now; I had to make good, and figure it out. 67.198.37.16 (talk) 19:47, 11 November 2020 (UTC)


 * p.p.s. Looking at the article, two things are clear: the statements about irreversibility are pure unadulterated bunkum, and must be removed. The second is that the title of this article is incorrect, it should be introduction to entropy in thermodynamics because it utterly fails to touch even the tip of the iceberg of entropy, for example, how did those biologists know how to compute the entropy of immunoglobulin of zebrafish? Entropy in thermodynamics is a tiny, itty-bitty corner of the big-wide-world, these days. It's a drop in the bucket of what we know about, what we can say about entropy. 67.198.37.16 (talk) 20:24, 11 November 2020 (UTC)


 * p.p.p.s. I just now typed in "Katok Entropy" into search engine and the very first hit is this PDF: FIFTY YEARS OF ENTROPY IN DYNAMICS: 1958–2007 JOURNAL OF MODERN DYNAMICS VOLUME 1, NO. 4, 2007, 545–596 WEB SITE: http://www.math.psu.edu/jmd sorry for all-caps, that's cut-n-paste. A proper article on "introduction to entropy" would take that article as a base outline, and somehow reduce it to 2-3 pages. That is what entropy is. 67.198.37.16 (talk) 21:01, 11 November 2020 (UTC)


 * Thank you, Editor 67.198.37.16 for your comment. Again I say that I would feel more comfortable chatting with you if you were very kindly to give youself an ordinary Wikipedia user name. I suggest you preserve your privacy by choosing a Wikipedia user name that hides your personal identity. If you do that, then, so far as I have found, it is secure to contribute to Wikipedia.


 * The current of opinion on this page so far is that thermodynamic entropy is distinct from statistical mechanical and from mathematical and from informatic entropy. The present current of opinion is that thermodynamic entropy should lead the present article, with the article title being changed to Introduction to thermodynamic entropy.


 * There is an article Entropy (information theory), and a fair number of various other articles with the word 'entropy' in their titles.


 * If you feel that those articles need an introductory article or some introductory articles, perhaps now is your chance to write one of more of such.Chjoaygame (talk) 13:33, 12 November 2020 (UTC)


 * Yes, I agree, rename it to Introduction to thermodynamic entropy. As to it's being "distinct", yes and no. It's "distinct" in that it corresponds to what intro textbooks in physics and chemistry might say. As to it being a conserved geometric quantity, similar to some other geometric invariant, say for example the homotopy groups or gauss-bonnet, or rigidity results, no, it is not distinct. The current understanding of microstates in physics date back 100 years, and it hasn't really changed much or at all, and so its clearly "the same" entropy as all the others, and so in that sense it is not "distinct". Clearly, this article as currently written does not even attempt to provide a rosetta stone to the other languages. Now if you were to start making arguments about topological entropy or metric entropy, that would be different... and interesting.


 * I admit I was mislead by the title. Other than that, I guess it's OK, except that it makes patently false statements about order and disorder, and false statements about irreversibility.  Those should be removed.  I have no particular burning desire to edit this article. I was responding to a call at WP:Physics. You can find out my real name, who I am, and the kinds of articles that I edit, by looking at my talk page. I refuse to edit under a login name, as that is an invitation to be attacked by kooks and cranks. WP is a fairly hostile environment. 67.198.37.16 (talk) 19:18, 12 November 2020 (UTC)


 * Agreed that the article is flawed. It won't be too easy to get it right. I will comment further on my talk page.Chjoaygame (talk) 22:00, 12 November 2020 (UTC)


 * Regarding the survey article by Katok - It is excellent! I agree, it could be used as a guide to our introductory article. I also note that in the beginning, the following phrases occur (Emphasis mine):


 * "the word entropy...was introduced in an 1864 work of Rudolph Clausius, who DEFINED the change in entropy of a body as heat transfer divided by temperature, and he postulated that overall entropy does not decrease (the second law of thermodynamics)."


 * "While entropy in this form proved quite useful, it did not acquire intuitive MEANING until James Maxwell and Ludwig Boltzmann worked out an atomistic theory of heat based on probability, i.e., statistical mechanics, the “mechanical theory of heat”."


 * "Boltzmann’s DESCRIPTION of entropy was that it is the degree of uncertainty about the state of the system that remains if we are given only the pi, (i.e., the distribution or macrostate).


 * In what follows in the article, the term "entropy" always refers to Shannon's information entropy. Again, we must maintain the distinction between thermodynamic entropy and the use of information entropy to explain it.


 * Regarding the zebrafish, even biologists know how to correctly compute the INFORMATION entropy, as the log of the phase-space volume, these days. Did Boltzmann's constant ever enter into their analysis? If not, then their analysis was entirely informational, and apparently very productive, good for them. But if Boltzmann's constant was not part of their analysis then they were not dealing with THERMODYNAMIC entropy, which is the subject of this article. Entropy in thermodynamics may be a tiny, itty-bitty corner of YOUR big-wide-world, these days, but it may not be so itty-bitty in some other people's world, like anyone who designs anything that requires considerations of heating or cooling, without needing a statistical mechanical explanation of the process. That includes experimental chemists, designers of cars, appliances, engines, motors, ... oh never mind, the list is enormous. And, seeing as how this itty-bitty article is about thermodynamic entropy, it should do its level best to introduce a beginner to just that. PAR (talk) 06:55, 13 November 2020 (UTC)


 * Now that the article has been renamed, my objections fall moot. About half my editing on WP consists of providing simple, easy-to-understand informal explanations of otherwise dense and opaque topics, and I applaud efforts to make articles easier to understand by a broader audience. It's a good thing.

From the physics point of view, thermodynamic entropy is "explained" by "information" entropy; the explanation is provided by the microstate theory of matter (atoms in a liquid bumping into each other, etc.). The "information" entropy is in turn "explained" by geometry; entropy is a property of geometric shapes, see for example, Morse theory; some textbooks in Riemannian geometry touch on this. The idea of "things bumping into other things" (e.g. atoms bumping into one-another) can be expressed in terms of graphs (say, a vertex for every bump, and an edge from one bump to the next), and so one can express entropy on graphs (a famous example is given by sand-piles; each vertex is a grain of sand, each edge is the other grains of sand that it touches. See Abelian sandpile model. But also the petroleum industry uses percolation models to estimate flow of oil from fraking, etc.). This is not unlike homology, where you can abstract away the common elements of the half-dozen different homology theories, and formulate an abstract version on graphs. After that, it gets interesting: many graphs occur as the results of grammars and languages, and so one can assign entropies to that (this is partly what the biologists were doing, probably without fulling realizing it: DNA encodes 3D structural shapes, which interact based on their shapes, via electromagnetic interactions between the electrons in atomic orbitals. This is called the resonant recognition model of how proteins interact via electromagnetic fields (see resonant interaction). They are "bumping into" one-another, not unlike the atoms in an ideal gas, although the "bumping" is more complicated, because the atoms in an ideal gas are point particles with spherical symmetry, but amino acids are not. So if you want to compute the "thermodynamic" entropy of something that isn't simply round and sphere symmetric, you have to deal with the shape of the thing that is bumping, and you have to deal with non-local forces, e.g. van der Waals forces, and with asymmetric forces, which is what the resonant recognition model does. Oh wait, there's more! Suppose you wish to compute the thermodynamic entropy of a mixture of two different gasses, say helium and neon. You have to adjust for the proportion of each. And so here, different amino acids occur in different proportions. And they float in a soup of water at some temperature. If you wish to deal with the thermodynamic entropy of freon vs ammonia, you have to deal with shapes. If you pull on that thread, you again find that shapes are described by grammars and languages, which, in earlier decades, was the traditional domain of computer scientists and of linguists, respectively. 3D shapes, you could say, are a special case of "language"; in atomic physics, they express the "grammar" of quantum orbitals of atoms. I mean this in a literal sense, and not as a poetic allusion. You can write Backus-Naur forms for how atoms interact; when you do this, you get things like Lindenmeyer systems, and thence onwards to algorithmic botany. (redlink, see algorithmic botany website) So the language and grammar of atoms is fairly well-understood, and the means to compute the "information" entropy of languages and grammars is somewhat understood, How this "information" entropy depends on the analog of "temperature" e.g. similar languages given a Zariski topology, and how this abstract entropy realizes itself in the 3D shapes of molecules is kind-of partly understood, and how to compute the "thermodynamic" entropy of 3D shapes (proteins) in a soup of room-temperature water is kind-of understood. Again, see the resonant recognition model redlink for details. So this is all very pretty, it is a tour of how we go from "entropy as a geometric invariant studied by mathematicians" to "entropy that classifies the motion of things in the spacetime we live in studied by physicists" to "entropy of grammars and languages studied by biologists". When scientists talk about entropy, these are the kinds of things they talk about. These are the kinds of things that could/should be sketched in an "intro to entropy" article. 67.198.37.16 (talk) 20:01, 13 November 2020 (UTC)


 * I am interested in this idea of "entropy is a property of geometric shapes", but looking at Morse theory, I see no reference to entropy. I'm also interested in "one can express entropy on graphs" but looking at Abelian sandpile model I see no reference to entropy. Also, I am interested in your statement ""entropy as a geometric invariant studied by mathematicians". Do you have any references that would help me understand these concepts?


 * Also, I am very interested in the question of temperature. In thermodynamics, temperature is the conjugate variable to thermodynamic entropy, their product being part of the fundamental equation for conserved energy: dU = T dS + etc. Is there an information-theoretic analog of temperature?. In thermodynamics, introducing the conservation of energy gives the link between thermodynamic entropy and thermodynamic temperature. Information theory does fine with information entropy, but can we say, in a purely information theory sense, no reference to thermodynamics, that the introduction of some conserved quantity yields an information-theoretic analog of temperature? Thanks. PAR (talk) 20:31, 14 November 2020 (UTC)

Page Rename
It appears that everyone agrees that the page should be renamed, so I did it. PAR (talk) 05:06, 13 November 2020 (UTC)


 * Good move. How exactly did you do it?Chjoaygame (talk) 05:33, 13 November 2020 (UTC)


 * I hit the "move" button at the top, between "history" and "unwatch" and filled in a new title. Didn't touch the other buttons. Also read this: . PAR (talk) 06:03, 13 November 2020 (UTC)


 * Thank you.Chjoaygame (talk) 07:28, 13 November 2020 (UTC)

Commentary
In order to avoid messing up Editor PAR's nice new start, I am commenting in this section, which I may regard as parenthetic. I would like to say that I think that the words 'spread', 'disorder', and 'missing information' are not respectively on the same footing, whatever 'footing' might mean.

For me, 'spread' has a distinctly physical footing. I know how to spread butter on toast. I can do it with my hands. Descartes' res extensa. Indeed, spreading and extending have a lot in common.

For me, 'disorder' has a mentalistic as well as a physical footing. Yes, one can disorder things with one's hands. But it is hard to avoid a mental aspect to guiding the operation. A mixture.

For me, 'missing information' is purely abstract. It's all in the mind; I don't see a physical meaning in it. Descartes' res cogitans.

I think it would be good to let these distinctions be clearly apparent in the article.Chjoaygame (talk) 10:57, 18 November 2020 (UTC)

As for the current second and third paragraphs of the lead, I would like to make an assertion about the following.


 * ...the second law of thermodynamics, which says that in an isolated system (a system not connected to any other system) which is undergoing change, entropy increases over time.


 * Entropy does not increase indefinitely. As time goes on, the entropy grows closer and closer to its maximum possible value. For a system which is at its maximum entropy, the entropy becomes constant and the system is said to be in thermodynamic equilibrium. In some cases, the entropy of a process changes very little.

I think this is a viciously dangerous blind alley. Yes, a blind alley that attracts many who are walking along the street, but still viciously dangerous.

It seduces into the idea that thermodynamic entropy is defined for a body that is not in its own state of internal thermodynamic equilibrium. The key to thermodynamic entropy is the unique extremum of symmetry that belongs to thermodynamic equilibrium. Thermodynamics does not describe the time course of actual physical processes. Non-equilibrium thermodynamics is a work in progress, which hasn't circumvented the fact that thermodynamic entropy is an equilibrium concept. To seduce beginners into dismissing that is to lead them into a vicious blind alley.Chjoaygame (talk) 11:25, 18 November 2020 (UTC)


 * Regarding the three ways of trying to conceptualize entropy, I agree. They are not all on the same footing. I only lumped them together because they are all attempts tho conceptualize entropy. I was thinking of a section discussing all three, including their unequal footing. Regarding your objection concerning equilibrium, I also agree, it is strictly true, but there is the approximation often made of local thermodynamic equilibrium (LTE) which, strictly speaking, cannot happen. Also there is the idea of the chemical reaction rate. I am more familiar with these approximations because without them, my job building computer models of physical systems would be much less productive. I mean, if we are to be that strict about things, the phrase "entropy always increases" has no meaning. Also, what do you see as the "viciousness" that happens when one strays from the strict interpretation and how can we convey an intuitive sense of change? PAR (talk) 15:52, 18 November 2020 (UTC)


 * Are you saying that LTE and chemical reaction rates are not part of classical Thermodynamics. On that I might agree, but do they (in simplified form) belong in this article? Is it admissible to say that entropy increases for the purposes of this introductory article? PAR (talk) 16:33, 18 November 2020 (UTC)


 * Thank you for your thoughtful comments, Editor PAR. Could the article somehow use a metaphor of stepping stones across a stream, at least tacitly in our own minds, if not explicitly in the article? Going from stepping stone to stepping stone doesn't obliterate an idea of time.


 * As Editor PAR has observed, Einstein celebrated thermodynamics as beyond overthrow. But Einstein reserved that it has a definite scope of applicability. Science, even physics, is not yet omniscient. Tomorrow perhaps, but not today. I think it vicious to try to present oneself as omniscient, however subtly, though Clausius' talk of "the universe" stands as a perpetual and effectively seductive temptation to do so. Wikipedia ought not propagate an idea of omniscience, nor help other people to do so.


 * As Editor PAR has observed, such approximations as that of local thermodynamic equilibrium are very valuable. I think it doesn't detract from their value to say explicitly that they are approximations. Indeed, I think it clarifies thought about them. An important part of science is expression of the logical steps in its conceptual structure.Chjoaygame (talk) 03:13, 19 November 2020 (UTC)


 * Stepping stones, yes! Stepping through time would be the temporal equivalent of LTE, which is a spatial approximation. I agree, LTE, etc. are approximations and, if mentioned, should be described as such. PAR (talk) 04:45, 19 November 2020 (UTC)

Shannon's function
In my view, the name 'quantity of information' is an unfortunately misleading term for Shannon's function, especially in the present context. Yes, it is historically customary or traditional, and one can shoehorn in the name, but at the risk of making it seem that 'quantity of information' is 'quantity of knowledge' or 'quantity of ignorance'. The presently relevant meaning of Shannon's function is nearer to 'extent of longwindedness' than to 'amount of knowledge'. I think that 'spread' is a better ordinary language word  for Shannon's function than is 'information'. There is no requirement for a longwinded signal to convey any knowledge. A longwinded signal can be either nonsensical or informative and still score highly on the Shannon assessment.

I think that the physically relevant informatic content of the Shannon function, originally used by Boltzmann, is to do more directly with Boltzmann's statistical mechanical concept of number of possible microstates. The idea here is to define 'microstates' so that all of a macrostate's accessible microstates are rendered equally probable. This is an exercise in fitting concision of coding. Shannon knew that the entropy of a signal is determined by the length of the code that achieves most concision, or least longwindedness.

I think that, since the aim of the present article is to guide the beginner's approach to thermodynamic entropy, one can avoid a blind alley by slipping past the traditional 'ignorance as missing information' interpretation of Shannon's function, and going more directly to an interpretation in terms of the extent of a set of a suitably chosen equiprobable microstates. The physically interesting and tricky bit is in the choice of how the accessible microstates are to be defined. That's an exercise in coding, where Shannon's function comes in.

One may consider a system described by its internal energy $$U(S,V)$$, with zero internal energy $$U(0,V)$$ and zero entropy $$S = 0$$ defined by reference to a state with zero temperature. To exclude thermodynamic work, one locks the volume $$V$$, and isolates the body through a rigid immovable adiabatic wall, except for a set of paddles within the body, that are to be agitated by shaft work from the surroundings, so as to transfer energy by friction within the body. Starting initially at temperature zero, and then raising the temperature slowly to reach the final intended entropy $$S_f$$, one adds a quantity of energy as heat $$Q_f = \int_0^{S_f} \mathrm d Q(S,V)$$ to reach the final entropy $$S_f$$ and final internal energy $$U_f = U(S_f,V)$$. In the body, some of this internal energy is in the intermolecular interactive energy, say $$\mathrm d X(S,V)$$, and the rest of it is in the kinetic energy of the freely moving molecular degrees of freedom, say $$\mathrm d W(S,V)$$, so that $$\mathrm d X(S,V) + \mathrm d W(S,V) = \mathrm d U(S,V)$$. The temperature $$T$$ is tied closely to the value of $$W(S,V)$$, as its density per unit volume. The entropy increment $$\mathrm d S$$ is determined by the ratio of $$\mathrm d Q(S,V) = \mathrm d U(S,V)$$ to the temperature $$T(S,V)$$. With suitable calibration and re-scaling, $$W(S_f,V) = \int_0 ^{S_f} \mathrm d W(S,V)$$ relates the entropy and the number of accessible equiprobable microstates.

Alternatively, one may consider a system described by its Helmholtz function, $$F(T,V)$$, with zero  Helmholtz function $$F(0,V)$$ and zero Helmholtz entropy $$S(0,V)$$ defined by reference to a state with zero temperature. To exclude thermodynamic work, one locks the volume $$V$$, and exposes the body, through a rigid diathermal wall, to a controlled temperature reservoir in the surroundings. Starting initially at temperature zero, and then raising the temperature slowly to reach the final temperature of the reservoir at temperature $$T_f$$, one adds a quantity of energy as heat $$Q_f = \int_0^{T_f} \mathrm d Q(T,V)$$ to reach the final Helmholtz entropy $$S_f = S(T_f,V)$$ and final Helmholtz  function $$F_f = F(T_f,V)$$. In the body, some of this Helmholtz function is in the intermolecular interactive energy, say $$\mathrm d X(T,V)$$, and the rest of it is in the kinetic energy of the freely moving molecular degrees of freedom, say $$\mathrm d W(T,V)$$, so that $$\mathrm d X(T,V) + \mathrm d W(T,V) = \mathrm d F(T,V)$$. The temperature $$T$$ is tied closely to the value of $$W(T,V)$$, as its density per unit volume. The entropy increment $$\mathrm d S(T,V)$$ is determined by the ratio of $$\mathrm d Q(T,V) = \mathrm d F(T,V)$$ to the temperature $$T$$. With suitable calibration and re-scaling, $$W(T_f,V) = \int_0 ^{T_f} \mathrm d W(T,V)$$ relates the entropy and the number of accessible equiprobable microstates.

Either way, no need to stretch the mind with talk of knowledge or ignorance. We should prefer a more physical viewpoint.Chjoaygame (talk) 17:15, 21 November 2020 (UTC)


 * The idea of entropy as a lack of knowledge as a "blind alley" is wrong, I think. Mathematically, Shannon's function


 * $$H = -\sum_i p_i \textrm{Log}(p_i)$$


 * where $$\sum_i p_i = 1$$, is just a mathematical function known as the information entropy (H). Mathematically, "information entropy" is just a meaningless name. The name takes meaning (which you apparently are not in favor of), and its value lies in its proper application to real world situations. These real world applications are where the various "ways of understanding" information entropy come in, and that revolves around the values, meaning and interpretation of pi as a probability. The idea of apriori knowledge is vital, part of which is the universe of possibilities that the pi as a whole refer to.


 * For example, Shannon's function H is maximised when all the pi are equal. If we have W discrete possibilities, each equally likely, then the information entropy is


 * $$H = -\sum_i (1/W) \textrm{Log} (1/W) = \textrm{Log}(W)$$


 * which is the same Log(W) found in Boltzmann's equation. Note that is subject to the apriori constraints of constant energy and particle number.


 * You mention "longwindedness". The minute you use that word, you are bringing in apriori knowledge to the situation which it would otherwise not have. "Longwindedness" is not an observation, it is a judgement. For example, consider all four-letter strings of the 26-letter alphabet (all lower case). There are 264 = 456,976 possibilities with an information entropy of about 18.8 bits (bits uses Log to the base 2). Most of them are not English words and are simply "longwinded" nonsense. By making this statement, I have implicitly divided the universe of possible 4-letter strings into longwinded nonsense and actual English 4-letter words that have "meaning". I have brought in a concept from the outside world which constitutes apriori knowledge. If I wish to only consider the universe of words that are meaningful in the English languange, I have severely limited the universe of possibilites. Suppose there are only, I don't know, 128 English words that are 4 letters long. If each is equally likely, then the information entropy is reduced to 7 bits, and none of them are "longwinded". I don't know if this is clear, but I am trying to remove your objection to information entropy as dealing mostly with "longwinded" nonsense. In each of the above cases, I am saying that the entropy is directly tied to our lack of knowledge, given the apriori constraints, which may not only constrain our probabilities, but also our universe of possibilities. Constraining the 4-letter strings to actually mean something, reduces our lack of knowledge from 18.8 bits to 7 bits. If we declare that the word must be part of a proper discussion of physics, then 4-letter curse words are eliminated, along with a lot of others, and our lack of information about that 4-letter string in this new universe is reduced even further, and H is less than 7 bits. If we declare (i.e. make the judgement) that German and French words, which would be classified as longwinded nonsense under the apriori English language restriction, are to be included as meaningful, the information entropy will be larger than 7 bits.


 * In every one of the above cases, the information entropy is directly tied to the idea of "lack of knowledge" by the fact that the number of bits of entropy is equal to the average number of carefully chosen yes-no questions you would have to ask in order to determine the exact 4-letter string that you are dealing with.


 * You speak about the idea that information entropy is maximized when the probabilities are maximally "spread out". This, of course, means spread out subject to apriori constraints. But when you try to give precise meaning to this vague notion of "spread out", the only precise definition is that the information entropy is maximized, subject to apriori constraints. It's much like "disorder". When you try to tie down what exactly that initially vague notion means, it winds up being that H is maximized subject to apriori constraints. When you try to give precision to the vague notion of "lack of knowledge", again, it is the maximization of H, subject to apriori constraints. These are all different "takes" on Shannon's entropy function as applied to the real world. The question is, which has the most intuitive value? I prefer the "lack of knowledge" idea, because it is so quantified by the idea of being the number of yes-no questions you have to ask about a system. For "spread" and "disorder", while helpful, the path to Shannon's entropy offers me no enlightenment. Nevertheless, of the three, the "lack of knowledge" idea gives the least physical intuition, but I take that lack as a challenge rather than a deficiency. PAR (talk) 18:12, 21 November 2020 (UTC)


 * Thank you for your careful thoughts. You present a clear 'right or wrong' viewpoint. I will submit that we are talking about a problem that I see as less cut-and-dried. As you rightly say, you "prefer" to read the Shannon function as about "lack of knowledge"; you have plenty of tradition to support that.


 * I accept that the matter can be shoehorned into a "lack of knowledge" piece of footware.


 * I think we agree, and have good literature support, that the 'disorder' interpretation is not helpful, except as a way of saying 'nothing to see here, move along please'. Many people urge it as "intuitive". Maybe intuitive in some sense, but I think not as a guide to understanding thermodynamic entropy; for that I see it as a sort of snow job.


 * We agree that "lack of knowledge" is lacking in ordinary physical intuition. We agree that to accept it would be to accept a challenge. I am reminded of Jaynes's "mind projection fallacy", without meaning anything specific or precise.


 * I am suggesting, however, that Shannon's function can be more physically interpreted as measuring spread, which I interpret in turn as having physical intuition. Perhaps you might be willing to reflect more favourably on this?


 * Entropy is measured directly by spread of energy as heat, using $$\mathrm d Q$$, using a mechanism that excludes transfer of matter. I think this is a very strong and almost unassailably intuitive physical intuition. I think this is a weighty factor for us.


 * I am here not trying to lock thermodynamic entropy exclusively into a 'spread of energy' reading; I am not sure about that. But I am much persuaded that the 'spread' idea is valid and physical. Matter tends to spread into unoccupied accessible space. Aristotle went so far as to say that nature abhors a vacuum. When matter spreads, it carries energy with it. Mixing increases entropy because of intermolecular binding energy, as observed by Gibbs in his account of perfect gas mixing.


 * I would say that taking the "lack of knowledge" viewpoint carries a lot of conceptual baggage. Perhaps you may be willing to look further at this?Chjoaygame (talk) 00:40, 22 November 2020 (UTC)


 * Shannon's function is a function of an argument that belongs to a complicated domain, the class of probability distributions suitably specified. That domain can reasonably be read as expressing 'quantity of knowledge', but I propose that such a reading is not a uniquely privileged interpretation. It is not built into the Shannon's function. Yes, Shannon's function is customarily or traditionally said to measure 'quantity of information', and information is often regarded as a carrier of knowledge. But I think that the 'quantity of information' reading already is a shoehorning, and that the 'quantity of knowledge' reading is a shoehorning of a shoehorning. True, Boltzmann shackled his formula with the 'disorder' reading. For our present purpose, we seem to agree that was a blind alley. One might say that I am proposing that, for our present purpose, Shannon's 'quantity of information' reading of his function, and Jaynes's 'quantity of knowledge' reading, are distractions from the merely combinatorial content of Shannon's function, and that the latter is enough for our physical problem.Chjoaygame (talk) 01:57, 22 November 2020 (UTC)


 * The whole idea is to intuitively link thermodynamic entropy to information entropy. We can get an intuitive understanding of thermodynamic entropy, and an intuitive idea of information entropy, but the crux of the matter is to intuitively join them as per Boltzmanns' equation. Disorder, lack of knowledge, spreading in probability space, these are intuitive takes on information entropy. I think lack of knowledge is the best take on information entropy, for the reasons I have given. Spreading of energy, or mass and energy, is an intuitive take on thermodynamic entropy and I can't think of anything better, although I'm not convinced its the best.


 * Are we talking past each other, or do you have a way of intuitively linking thermodynamic and information entropy? I think the mass/energy spreading idea does not do it. PAR (talk) 06:42, 22 November 2020 (UTC)


 * I agree that we should use the Shannon function to link the macroscopic and microscopic views of entropy. For a long time, I have followed the customary view, especially from Jaynes, though perhaps originally from Shannon, that the Shannon function can be regarded as measuring 'quantity of information'. Recently, thinking it over, in the light of the 'spreading' interpretation, I have found the 'quantity of information' view unintuitive or distractive.


 * I accept that your 'counting the bits' argument is admirable and helpful. But I think that can be read as a measure of spread, and that to bring in the idea of knowledge is more distracting than clarifying. I am proposing that 'spread' works nicely in both the physical and the probability distribution worlds, and that it provides a good natural link between them. It then seems redundant to bring in 'information' and 'knowledge'. Molecules spread without knowing it.


 * You rightly emphasise 'constraint'. The normal distribution is the one with the greatest Shannon function value, subject to the constraint of a given standard deviation. Then one asks 'why is the Shannon function the best measure of spread?' I think your bit counting argument is a good answer to that question. But I think that your bit counting argument makes good sense as viewed just from a coding or combinatoric perspective. Again, I think it redundant and distracting, even handwaving, to talk further there, about 'information' or 'knowledge'. Shannon was concerned with coding; I think that's enough.Chjoaygame (talk) 08:57, 22 November 2020 (UTC)


 * I am not familiar with the uses of 'entropy' in more abstract mathematical settings, but my limited acquaintance with them suggests to me that it refers to a geometrical property  of complex objects. For example, a friend of ours writes above "The "information" entropy is in turn "explained" by geometry; entropy is a property of geometric shapes." And "After removing what can flow away, what is left is the volume of the space that you take the log of, to get the entropy." And "As to it being a conserved geometric quantity, similar to some other geometric invariant, say for example the homotopy groups or gauss-bonnet, or rigidity results, no, it is not distinct." I have the impression that it measures a kind of extent, volume, or spread. I have the impression that, in those contexts, the ideas of information and knowledge are not called upon. Yes, they can be brought into the picture, but I think they are not esseential in those contexts.Chjoaygame (talk) 10:53, 22 November 2020 (UTC)


 * Perhaps it may help to say that what distinguishes the macroscopic from the microscopic is the respective quantity of code that would be required for a full specification of them. The macroscopic specification uses very little code, while a full microscopic specification would require a vast quantity of code. This brings us directly to coding theory while avoiding more anthropomorphic terms such as 'knowledge' and 'information'.Chjoaygame (talk) 16:37, 23 November 2020 (UTC)


 * Yes, that's the point I was trying to make when I said that Shannon's function is just a function, but the interpretation of the Pi as probabilities is a real-world application. Interpreting the Pi as probabilities unavoidably brings in the concept of "knowledge". P2=1 means that outcome number two is certain. I need to understand the geometric entropy that you mentioned before I can talk sensibly about it.


 * The identification of entropy with spatial spread brings difficulties (to me, anyway). You can have the probability of a particle being 1 meter from the origin and another probability of it being 2 meters from the origin, and if that exhausts all possibilities, then P1+P2=1. The entropy is the same if instead of 1 and 2 meters, you have 100 and 200 meters, but the standard deviation is 100 times greater in the second case, so entropy does not measure spatial spread, while the standard deviation does. I can see it as a "spread" in probability space, but not in physical space.


 * If you think the section on "spreading" is inadequate, wouldn't it be better for you to edit it? I mean, while keeping it simplistic, without jargon?


 * P.S. On this note, I found the concept of entropic uncertainty versus Heisenberg's uncertainty very interesting. Entropic uncertainty is, of course, based on entropy, while Heisenberg's is based on standard deviation, basically. Entropic uncertainty is apparently more informative that Heisenberg's. Again, "uncertainty" appears to fall into your definition of anthropomorphic. PAR (talk) 03:17, 24 November 2020 (UTC)


 * I don't see the concept of probability as necessary in this topic. Yes, it is very conventional. It is a conventional prop to understanding to talk about probability in this context, but I think it distracts from the real physics, another blind alley.


 * The reason for irreversibility is that one starts the process with a short description, in terms of thermodynamic variables of state. And one ends it with another such description. One has not specified the states in terms of the full molecular descriptions, which are voluminous. So one cannot expect to be able to reverse the process, because to do so, one would need to feed the initial and final molecular descriptions to one's 'reversing machine'. It is not so much a matter of what one knows, as of what one has specified. At least in the case of classical statistical mechanics, the actual process goes along according to the laws of nature, not according to some probability doctrine, or some doctrine of knowledge. (I do not wish to rise to the intellectual heights beyond the classical case.) So I think that probability is an interesting, but ultimately redundant, or even misleading, ingredient in the conventional story. I think the physical story is adequately and better told by the quantities of code in the various descriptions. Yes, you can say that the descriptions exhibit information or knowledge, but I propose that such does not add to the physics. I propose that it is an interesting though perhaps distracting interpretation, but not a directly physical account. The descriptions of the states are directly physical accounts, and are adequate.


 * The Shannon function is a function of a class of descriptions. It happens that convention has viewed that class as probability distributions, but I think if it had stuck to the descriptions themselves without being distracted into talk of probabilities, we would not be writing this article. The topic would be done and dusted, home and dry, without the air of mystery that currently clings to the 'concept of entropy'.


 * The Shannon function measures a sort of syntactic spread of its argument descriptions. Syntax is a coding concept.


 * I think that your story that is intended to debunk the spread view is a carefully chosen but inappropriate account of the situation. I think is fair to observe that a gas that starts confined in a corner of a large box, and then, by a thermodynamic operation, is released, will spread throughout the volume of the box. Such is an irreversible process accompanied by an increase of thermodynamic entropy. It is spread in physical space.


 * I agree that the entropy of a distribution is not the same as its standard deviation, but the mere mathematical entropy of a probability distribution is not a thermodynamic quantity. To make it into a thermodynamic quantity, an additional specifically physical ingredient is necessary, witness Boltzmann's constant.


 * I think it relevant that the mathematical concept of entropy as a geometric property is no mere accident. In some crude sense, to be corrected by an expert, it measures some kind of qualified volume or area.


 * As for probability being necessarily about knowledge, yes, we Jeffreys–Jaynes supporters like that idea, but we know that many authorities on probability theory are keen to avoid it, and are keen 'frequentists'. While we may regard their viewpoint as unduly restricted, we cannot deny that they get along happily enough for many of their problems. For our present problem, I think we don't need the knowledge interpretation.


 * As for me editing the article, I generally don't want to, except for special circumstances that I can't predict.Chjoaygame (talk) 05:24, 24 November 2020 (UTC)


 * My example was not intended to debunk the spread view. It is an example that bothers me when trying to justify the spread view. Here is another example: Suppose we have a crystal of some substance, and the atoms or molecules are not essentially point particles, but rather have rotational degrees of freedom as well. Suppose, to begin with, none of the particles are rotating. The energy is not equipartitioned among all degrees of freedom. After some time, equipartition will practically occur and the particles will be rotating as well as vibrating at their locations. The entropy of the former case is lower than the entropy of the latter. While I see "spread" of energy into rotational degrees of freedom, which is spread in phase space, I see no physical spatial spreading of mass or energy. PAR (talk) 02:24, 25 November 2020 (UTC)


 * Yes, your point is good in some respects. But such a case is very special. The non-equilibrium initial state is not within the scope of the second law of thermodynamics, which covers just initial states in which the bodies of the system are each in their own internal states of thermodynamic equilibrium. The virtual substate constituted of the rotational degrees of freedom, if exactly as you specify, would have its virtual temperature at absolute zero, which would be a problem.


 * From a more general viewpoint, your concern seems perhaps reasonable. Can we construct examples that may help? You point is that one can easily find processes of obviously physical spread, but perhaps there may be processes in which the idea of physical spread, either of matter or energy, doesn't work, and which require resort to an abstract kind of 'spread' in phase space? You are not keen on using the word 'spread' for such processes, or at least you propose that is not good to say that such 'spread' is physical.


 * We are working in a context of the second law. So our initial states must be of bodies or compartments in their own states of internal thermodynamic equilibrium, separated from each other by walls of definite permeabilities, and isolated from the surroundings. Our exemplary process will be initiated by a thermodynamic operation that increases the permeabilies of one or more walls, or that involves some force being imposed from the surroundings by an external agency.


 * Let us first consider the case of just change of permeability of internal walls. Except for trivial cases, there will occur transfer of matter or energy between the bodies until the new permeabilities are closed off. I think that would be ordinary physical spread. Next let us consider a case proposed by Gibbs. Two bodies of equal volumes at equal pressures and temperatures of differing ideal gases in their respective internal thermodynamic equilibria are initially separated by an impermeable wall. The wall is removed and the mixing gases are forced slowly by the surroundings into just one of the volumes. The entropy of such mixing is zero, when it is defined to allow for the work done in forcing the mixture into the one final volume. Indeed there has been no spread within the bodies in an ordinary physical sense. But I think one might say that energy has 'spread' from the surroundings into the combined bodies, and that accounts for the non-mixing increase of entropy.


 * These two attempts, to produce an example of the kind of process that we are looking for, have failed. Perhaps we may succeed if we keep trying?Chjoaygame (talk) 05:11, 25 November 2020 (UTC)


 * When I said that all of the particles had no rotation, that was extreme and yes, the resulting zero temperature is a problem. All we need is to say that the rotational degrees of freedom are "colder" than the vibrational. So the main objection is that such a state must be an equilibrium state, and then something changes and the system proceeds to a new equilibrium state with higher entropy. Just to be clear, it's not that such an initial state cannot exist. By Poincare's recurrence, it will eventually happen, just as will all of the gas in a container spontaneously moving to one quadrant of the container. The problem is that such a state is not an equilibrium state. It would be nice if we could figure out what the equivalent of a "wall" would be in this case, one that maintained the different temperatures, and is then made thermally conductive, in order to have an example that debunks the universality of the physical spreading concept. However, the only way to support the spreading concept, in this particular case, is to show that, in principle, no such "wall" can exist, and I doubt that can be done. I have to think about it. PAR (talk) 05:57, 26 November 2020 (UTC)


 * I found your proposal helpful. It lit up the fact that in a body in its own internal state of thermodynamic equilibrium, the constituent particles must be interacting with one another in an enclosed region of space that they share. An interesting example is in Planck's body of radiation contained by rigid perfectly reflective walls. In Planck's original version, an arbitrary state would persist out of internal thermodynamic equilibrium until a small grain of carbon was introduced to 'catalyse' its establishment. In Planck's original version, the photons did not actually interact with one another; with no wall separating them, they stayed out of joint internal thermodynamic equilibrium. At temperatures above zero, molecules radiate occasionally, as well as colliding. Black body radiation coincides with a Maxwell–Boltzmann distribution.


 * An equilibrium state is not an instantaneous state. It has duration. It includes interaction. Its state variables are defined as time averages.Chjoaygame (talk) 18:27, 26 November 2020 (UTC)


 * Its a good example, but still, it does not begin with an equilibrium state, even though it has duration. Also, there are very small photon-photon interactions so even without the carbon granule, these interactions will produce a Planck distribution, it just might take 100 years or more. The carbon granule is analogous to a chemical catalyst. PAR (talk) 18:49, 26 November 2020 (UTC)

paragraph
Thinking it over, I would summarise my proposal as saying that the statistical mechanical account of the second law can be expressed in terms of combinatorics or coding theory. For our purpose, it is not necessary to interpret those in terms of probability. Moreover, if it is desired, nevertheless, to make a probabilistic interpretation, it is not necessary to have recourse to the full hand of the Jefferys–Jaynes framework, that explicitly goes beyond the powers of the frequentist doctrine, by dealing with the probabilities of such objects as hypotheses, for the sake of statistical inference. We are not attempting statistical inference to gain knowledge. One of our guiding ideas for this article is simplicity, or perhaps conceptual parsimony.Chjoaygame (talk) 05:11, 25 November 2020 (UTC)

Thinking it over some more. Our IP friend may have some input here, even though he is not interested in thermodynamics. For the microscopic account of thermodynamic entropy, there are various ways to go. One is Boltzmann's method of counting states, as a combinatoric or as a coding problem, or as a probabilistic problem. Another recognises that an isolated classical system takes a deterministic trajectory around its phase space. The trajectory more or less occupies some kind of 'volume' in the phase space. That 'more or less occupied volume' is measured by mathematical 'entropy'. The Poincaré recurrence theorem belongs there.Chjoaygame (talk) 14:24, 25 November 2020 (UTC)

A possible three sentences:
 * Thermodynamic entropy is a measure of the spatial spread of energy or matter in a body. When two bodies are brought together so that they interact, energy or matter spreads from one to the other, and the sum of the bodies' entropies increases. This fact is recognized in the second law of thermodynamics.

No mention of microscopic particles or photons.Chjoaygame (talk) 02:04, 26 November 2020 (UTC)

I think our fundamental problem is as follows.

In classical physics, which were good enough for Boltzmann, the thermodynamic equilibrium macrostate of the system can be regarded as represented by a suitable class of trajectories in the phase space of instantaneous microscopic states. As a first guess, we may suppose that any such trajectory, chosen arbitrarily, is adequately characteristic of the thermodynamic equilibrium macrostate of the system, we might say as 'generic'. Perhaps there are infinitely many such generic trajectories; this is a matter for discussion by mathematicians. Another matter for mathematicians is to measure the 'volume' of phase space occupied by such trajectories; a suitable parameter for such volume is to be called the 'microscopic entropy'; Shannon's function may have its place here. For discreteness within a trajectory, we may suppose that we can specify it by points separated by a suitably fixed short time step.

Our general idea might be that no matter which point we choose on which trajectory, its microscopic instantaneous state will have all the relevant equally weighted averages for the thermodynamic equilibrium macrostate. Alternatively, and I think more intuitively and directly physically for thermodynamic equilibrium, we may have the general idea that any arbitrarily chosen trajectory, when followed for a long time, perhaps a Poincaré recurrence time, and averaged over equally weighted time steps, will have all the relevant averages for the thermodynamic equilibrium macrostate. The physical problem is to choose the suitable class of trajectories, using the laws of mechanics. Though this can be analyzed probabilistically, such is an interpretation, not straight physics. The probabilistic interpretation is traditional amongst the technical cognoscenti, but it is really a way of tackling the mathematical problem that is now outmoded by improved mathematical methods, as indicated by our IP mathematical friend. For the newcomer, the probabilistic interpretation is an unnecessary, and indeed unhelpful, technical and conceptual hurdle, beyond the straight physics. For the newcomer, the straight physics is simpler and preferable.Chjoaygame (talk) 22:36, 29 November 2020 (UTC)


 * I'm not sure that I'm following your point here; would you mind clarifying a little?


 * FWIW, I'm not sure how Poincaré recurrence time is practically relevant here. For a macroscopic system, the probability of, for example, heat spontaneously flowing from a cold object to a hot object is so low that the expected time for returning to an initial state out of thermal equilibrium is something like $$10^{10^{23}}$$; this is so large that the units don't matter at all—they could be anything from Planck times to Gyr and it's still basically the same (impossibly long) period of time. Poincaré recurrence might be an interesting consideration from a theoretical standpoint, but I'm having a hard time seeing its relevance to a conversation about providing a conceptual overview of entropy that's accessible to the uninitiated.  Thanks for any clarification you can offer! DrPippy (talk) 02:47, 30 November 2020 (UTC)


 * Thank you for your thoughts.


 * Thermodynamic equilibrium is a steady state that lasts a long time. Thermodynamic entropy is defined on the basis of thermodynamic equilibrium. During that long time, the phase space point in instantaneous state space explores practically the whole of that space. In other words, the trajectory spreads over phase space. This is why the 'spread' over 'accessible state space' interpretation of Edward A. Guggenheim is so apt and intuitive. To calculate the entropy of the state, one averages over the whole time of such exploration. A thermodynamic process, such as is contemplated by the second law, usually starts and ends with thermodynamic operations that change the permeabilities of the walls between the participating subsystems. That operation makes new states accessible, and the systems spread into them, increasing the total entropy.


 * In the past, especially in the traditional Boltzmann interpretation, using classical mechanics, the algorithms or schemes known for calculation of such averages were thought of in terms of 'probability'. Yes, indeed, probability conceptions, setting up various traditional sample ensembles, may be suggestive and helpful as inspirations for mathematical algorithms. But as pointed out by Edwin Thompson Jaynes, using the language of "the mind projection fallacy", the trajectories are determined by Newtonian mechanics, not by what algorithmic scheme the physicist might find handy, reasonable, or persuasive; the microscopic particles cannot read the physicist's mind. The trajectories explore practically the whole of their accessible phase 'space'. The mathematical entropy of a trajectory is an index of how much it occupies of virtual or phase space over the duration of the trajectory. This view avoids the conceptual complications of probabilistic algorithms and is purely physical. The actual calculation and algorithm is a mathematical problem, not a physical problem. The relevant mathematics was not available to Boltzmann, but is available today. For the understanding of the concept of thermodynamic entropy in microscopic terms, the newcomer should be exposed to the physics without the unnecessary and conceptually profligate distraction of highly technical but physically irrelevant mathematical tasks.


 * Earlier in this discussion, we had the benefit of the opinion of an expert mathematician whose attention was focused entirely on the mathematics, and who was not interested at all in thermodynamic entropy. But when he was interested in this article, he wanted it to ignore what he saw as the nonsensical notion (I think I understood him aright) of thermodynamic entropy as it related to irreversibility. When the turn of the discussion changed the title to 'Introduction to thermodynamic entropy', he left for greener pastures. But he was an expert in the mathematics that I am talking about. In order to reverse a thermodynamic process, it is necessary to specify exactly its initial and final microscopic states. Such specifications are not available in the macroscopic thermodynamic description. It is the choice to specify the states through macroscopic the description that makes the process irreversible. Perhaps the physicist knows the microscopic specifications, but it is not what he knows that matters; it is how he chooses to deploy the specifications. Of course it is practically impossible for the physicist to know the specifications, but that is not relevant for the conception microscopic of entropy. It is relevant, of course, for the second law and for the concept of irreversibility, further matters that go beyond the definition and conceptualization of microscopic entropy, and can be dealt with on their merits.Chjoaygame (talk) 05:26, 30 November 2020 (UTC)

New Introduction
Just to get things started, I rewrote the introduction, trying to keep it simple, mostly correct, and with few logical blind alleys, trying to incorporate what has been discussed. I will not be offended by modifications, or a complete reversion, if necessary. I'm just trying get the ball rolling. I think there should be another section entitled something like "Other approaches to understanding entropy", in which the concepts of spreading, disorder, and missing information would be discussed. PAR (talk) 07:46, 18 November 2020 (UTC)


 * I generally like it, thank you. I do feel that in the first paragraph, we need to throw a bone to the people who have seen the word in a popular context and are looking for a quick definition and aren't really interested in physics. This reminds me of a dispute I was involved in regarding the article Asian giant hornet. All year there have been headlines referring to them as "murder hornets," and some of us wanted to get a mention of that nickname in the first paragraph, to signal to lay readers that they were in the right place. However several entomologists were downright offended by the nickname and refused to allow it, on the grounds that no reliable source in entomology recognized "murder hornet" as a common name. Finally a compromise was reached whereby the nickname is mentioned at the end of the first paragraph, while also acknowledging that it's not a recognized common name. So, I've attempted a similar treatment here. Not everyone is a trained physicist, and the word "entropy" is out there in the public consciousness — just Google it. For just one sentence of the article, let's help out the non-physics readers and not be too terribly uptight about it.  -Jord gette  [talk]  17:13, 18 November 2020 (UTC)


 * I see your point. I added a footnote to your edit to the later section entitled "introductory descriptions of entropy". I think this section is where we can elaborate on the various popular "takes" on entropy. PAR (talk) 04:39, 19 November 2020 (UTC)