Talk:Entropy/Archive 3

entrepein
I have a book which says Clausius derived the term entropy not from "entrepein" but from "en tropei" (both Greek) meaning change.

Infinite Universe
(Copying this here out of archive2 so it doesn't get overlooked, because I feel this was never properly resolved, and I for one still feel quite uncomfortable about these edits of Paul's Jheald 09:21, 8 July 2006 (UTC))

Paul, you made several semantic edits which change the context and tone of the article, but you added no citations for any of them. Your edits, if properly cited, could provide a valuable educational addition to the article. If not cited however, they seem an awful lot like POV. Astrobayes 20:24, 22 June 2006 (UTC)


 * Dear Astrobayes, if I cited Einstein, would that be his POV? I think a good article should at the very least consider feasible alternatives and not tout one POV. To consider what happens in an infinite universe, would be a sensible hedging of one's bets. Paul venter 22:12, 29 June 2006 (UTC)

At the bottom of the Overview section, it reads that the second law does not apply to the infinite Universe, yet further down the article in 'The Second Law' section, it reads that the entropy of the Universe does tend to increase. Maybe I'm missing something, but this may need clarifying in order to properly state whether or not the Second law applies to the universe or not. — unsigned


 * Perhaps it was commenting on the fact that the second law states that entropy "tends to" increase - rather than always increases. Entropy doesn't always increase, it can decrease. However, the law states that in our humon observation, it usually increases. Fresheneesz 19:36, 29 June 2006 (UTC)


 * This is correct, and is in fact the crux of the entire concept of Entropy. Astrobayes 21:52, 29 June 2006 (UTC)

The jury is still out on whether the universe we live in, is finite in size or infinite. If it is infinite, the Second Law does not apply, if finite it would. Any statement about the entropy of "the Universe" increasing, is premature and speculative. My bets are with the infinite - you choose. Paul venter 21:28, 29 June 2006 (UTC)


 * Are you referring to an infinite "steady-state" universe, or an infinite "Standard Model" Big Bang universe, or an infinite Milne Model big bang universe? Any explicit statement about the entropy of the universe should describe explicitly what model is being used.


 * Some popular models today suggest that particles can spontaneously generate in the vacuum of free space. If this is a common agent for low-entropy energy sources... Even then, you'd have no decrease in entropy, though you might lower the entropy per particle.


 * You need to have some mechanism for decreasing the entropy of the universe. Black holes seem to be a pretty good candidate for performing such a task.


 * I was going to mention Milne Model cosmology as an example of an infinite universe, but now I realize that in this model, though infinite, it begins with a perfect almost crystalline pattern and from that state, entropy can only increase. So this may be a counterexample to your statement.  On the other hand, though the assumptions of this model are speculative, the results are very explicit, and a scientist should be able to get a long way toward thermodynamic analysis.
 * JDoolin 14:11, 23 August 2006 (UTC)


 * Why would the second law not apply in an infinite universe? Fresheneesz 20:52, 8 July 2006 (UTC)

Entropy and Information (FL platform)
Let me first say that I think the 8 lines or so that we have in the section "Entropy and Information Theory" currently in the article are (IMO) about right, and pitched at about the right level. I don't think there's any great need for change from this, either to emphasise or to de-emphasise the intuitive connection.

But I would like to offer a couple of comments (constructive, I hope) on some of the wordings that Frank was most recently discussing on the talk page now archived:


 * ====Response ====
 * I don't want to bother you in special areas such as "Entropy and Info Theory". My only concern is beginning students being hit with 'disorder' or with any introduction to Info Theory. Just to help them comprehend the very simple approach to the 3-4 old thermodynamic examples so they can go on to Gibbs and reactions is my life! I think your following comments are ALL constuctive. FrankLambert 20:21, 8 July 2006 (UTC)

1. kB
In his CalPoly discussion, Frank writes:


 * In sharp contrast, information ‘entropy’ depends only on one factor, the probability factor, -k Σ[Pi log Pi], where k is an arbitrary constant that never is required to involve energy, as does kB.

I think there's a danger that this can be taken the wrong way. As I tried to persuade Astrobayes earlier, there's no great significance to the fact that in Chemistry entropy is usually measured in Joules per Kelvin, and temperature in Kelvins, while Σ[Pi log Pi] is dimesnionless. One can entirely equivalently work throughout with the dimensionless entropy &sigma; = S / k, and the energy-scale temperature &tau; = kT.

Indeed, as I suggested to Astrobayes, &sigma; and &tau; are in many ways the more natural quantities, interestingly as Frank's friend Harvey Leff also expored in a recent paper, "What if Entropy were Dimensionless?", Am. J. Phys. 67, 1114-1122 (1999).  Not only does it more naturally reflect that the multiplicity, which is fundamentally what underlies entropy, is fundamentally a dimensionless variable. It also throws into relief that the crucial thing about temperature is the corresponding energy-scale quantity &tau; = kT. This is the amount of energy you have to put in to a system in thermodynamic equilibrium to get a unit increase in its dimensionless entropy &sigma;. That energy is greater for hot systems than for cold systems: energy flows from hot to cold, so for the 2nd law to be obeyed, the energy you need to add to a cold system to get a unit increase in dimensionless entropy must cause less than a unit decrease in the dimensionless entropy of the hot system. So working with &sigma; and &tau; makes it a little more transparent why the energy &tau; for an ensemble, defined by ðE/ð&sigma; (nearest I could find to a partial derivative "d") is the fundamental measure of its temperature.

To his credit, in what he wrote on the (archived) talk page, Frank adds a sentance that underlines this:


 * Further, merely substituting kB for k does not magically alter a probability of shuffled cards or tossed coins so that it becomes a thermodynamic entropy change

This is surely the point on no account to be obscured: one can freely move between S and &sigma;, and back again, without losing (or gaining) any physical meaning. There's nothing particularly special either way about choosing whether or not to include the extra factor kB, and therefore whether or not to work with S rather than &sigma;.


 * ====Response====


 * The foregoing is helpful in many ways. I, too, once thought and used an argument about thermo entropy having joules/K etc. But dimensions, in themselves are not significant, as you say. HOWEVER :-), it's the presence of ENERGY as the enabling aspect (component?) of a TWO-component totality of thermodynamic entropy that implicitly/always MUST have 'joules/K' that IS the differentiation between thermodynamic entropy and ONE component informational 'entropy'.


 * Thx for the pressing of the advantage of dimensionless sigma -- better than the understanding that I had. Excellent way -- for thermal physics that already has sigma front and center -- to prove 'hot to cold' is the 2nd law way! (For years, to show kids how obvious it is that energy dispersal from a hotter system to a cooler is the only way a positive entropy change occurs was using q/T [bold for large number for T] (for &Delta;S, hotter)to q/T  [smaller number for T] (for &Delta;S, cooler).


 * Also, although I salute Harvey re his dimensionless categorization of substances, since discovering 'dispersal', I've pushed viewing standard entropy values, and by yelling! that they must only be considered grossly/approximately/relative values of 'the energy that has incrementally been supplied the substance from 0 K to 298.15 K so that a particular substance could exist in that state' -- give far wider (and deeper) meaning to dozens of comparisons rather than just the old generalities about So differences in solid vs. liquid vs. gas. [Only way I beat Harvey!]) FrankLambert 20:21, 8 July 2006 (UTC)

2. Two "factors" energy and probability
Frank writes:


 * The two factors, energy and probability, are both necessary for thermodynamic entropy change but neither is sufficient alone

I have a problem with the word "factors", because of its mathematical association with multiplying two things together. Can I ask Frank for his reaction if I was to suggest that a clearer word might be "aspects"? Would the following equally capture the message that you're trying to convey:
 * "There are two essential co-equal aspects to thermodynamic entropy,
 * First the formula -Σ pi ln pi
 * Second that you are applying it to states that reflect dispositions of energies."

Am I right in interpreting that as your key message?


 * ====Response====


 * Thank you -- give me the best math 'read': "aspects", to me, gives a looser, more qualitative feel to what are vital separate [absolutely required ingredients FrankLambert 02:07, 9 July 2006 (UTC)] ...well, "components". Anything better than 'components'? ('Constituents' is too chemical, I think.)


 * Doggone, you love the math (and entropy would NOT be complete without that probability description for max energy distribution describing the 'actualization' FrankLambert 02:07, 9 July 2006 (UTC)) but I love the energetic little suckers that enable the math! And, pedagogically as much as my love, students starting the thermo chapter have been immersed in molecules...


 * So, I wish we could go with: [Omitting here, the part that I know is difficult for you to accept: "Energy of all types changes from being localized to become dispersed, if it is not hindered from doing so" ] "The overall process of an increase in thermodynamic entropy has an enabling component, molecular motional energy in an 'initial state' of a system. But actualization of any spontaneous entropy change requires removal of some constraint so increased numbers of energy distributions ("accessible microstates") are made available to the system -- a maximal probability under the new state conditions."


 * Somewhat OK? FrankLambert 20:21, 8 July 2006 (UTC)

Flipped coins, shuffled cards etc
There are a couple of points I might make here, but I've probably written enough for the moment to be going on with. Jheald 14:47, 8 July 2006 (UTC).

One other point with the CalPoly paper with its extensive discussion of "configurations" is perhaps to remember that properly applied to Classical mechanics, the states that statistical mechanics works with are configurations of the whole system in 6N-dimensional phase space, including momentum co-ordinates for each particle, not just the position co-ordinates. So, properly considered, the different possible molecular motions are always a consideration, even in the classical picture. (Even though we can sometimes useful separate that entropy out into different additive contributions, one from eg the permutations of impurities in a crystal, the other from other degrees of freedom, if the probability distributions are near enough independent). Jheald 14:47, 8 July 2006 (UTC).


 * ====Response====:


 * YES! YES!! Please tell me --I'm no way a stat mech guy or powerful in math, I just followed the babystat stuff in some phys chems, etc. and only from following, first, the development of the old Sackur-Tetrode and then, the cell models via which mixture entropy procedures were produced -- they smelled as bad as thermo entropy in shuffled cards...what thermodynamicists were doing was finding the CHANGE in the LOCATIONS of their cells. But THAT was exactly the CHANGE in the energy distribution, too!! And yet, no one that I could find talked about that.


 * Instead, maybe/probably because it fitted their preconceived notions that somehow entropy had to fit 'entropy is disorder' and here we have all kinds of new locations and by damn that's great disorder :-) [rather than seeing that in entropy evaluation, the primary goal is 'wha hoppens to the energy?']!


 * So that's how generations of chem students saddled with another confusing burden: two entropies. (And fooled Pauling in his evaluation of H2O residual entropy!) There's only one entropy -- whatever process maximizes the no. of accessible microstates (OK, measured by Shannon!) -- heating? Increased occupancy of higher energy levels. Gas expansion, mixing and all the rest? Increase density of energy levels. Does that float? or sail? FrankLambert 20:25, 8 July 2006 (UTC)

New First page of the article "Entropy"
I think it's best to work out differences on this Talk forum rather than insert and delete, etc. on the actual article page. So here's 1.3 pages of the Article that introduces the topic a bit more slowly, more pointed toward the young or mature reader not sharp in physics (and certainly not knowing calculus in the first line!)

So, following the present italics links to dismbig, infor entropy, entropy in therm/info theory:

In chemistry and physics thermodynamic entropy is an important ratio, a measure of the heat, q, that is transferred to or from a system when it is warmed or cooled by its surroundings. Only a small amount of q should be transferred (dq) at a specific temperature so that the temperature stays essentially unchanged. Then the process is reversible and the ratio is dq (rev)/T. German physicist Rudolf Clausius introduced the mathematical concept of entropy in the early 1860s to account for the dissipation of energy from thermodynamic systems that produce work. He coined the term ‘entropy’, that to him meant ‘transformation’, from the Greek word, trope, and added the prefix, en- to emphasize the close relationship of dq(rev)/T to energy. The concept of entropy is a thermodynamic construct, but the word entropy has been widely misused, e.g., in economics and fiction, because its thermodynamic relation to physico-chemical energy is blurred or even omitted. Legitimate linkages to fields of study are mentioned in sections that follow.


 * Comment 1: This article should define "entropy", not "thermodynamic entropy".
 * Comment 2: dq/T is a method to calculate a difference in entropy, not the entropy itself.
 * Comment 3: We shouldn't include too much history in the definition. These things should come in the History section or something.
 * Comment 4: Don't describe the misuse of the term here, in the basic definition. And don't present it in a so negative light. Fiction is for fun. And complaints about economics should be specific, or maybe avoided altogether.
 * Yevgeny Kats 18:06, 10 July 2006 (UTC)


 * Kats 1: Other uses/definitions are specifically referred to in the italics heading the article. This is the article dealing with thermodynamic entropy, as the previous lead sentence presented.
 * Kats 2: As eminent thermodynamicist Norman Craig has written in several places in JChemEduc, this is a common misunderstanding of entropy -- ignoring the third law. 'Entropy', when examined analytically always is actually 'entropy change', the result of a difference. Yevgeny, can you give me any instances in chemistry where an entropy 'value' is not actually based on its relation to 0 K, i.e., a difference?
 * Kats 3: Fine with me. I was just trying to follow the existing page as closely as possible but making it more layperson friendly, correcting a bit to conform with Clausius' actual words (and incidentally dropping in the word 'chemistry'!).
 * Kats 4: I think a warning is absolutely essential. The Britannica can be lordly, but Wikipedia should aid the ordinary serious reader as much as possible -- and as quickly from the start of its article as feasible. The average reader is not a scholar.  Is there any word in science that has been more misadopted by so many fields in so many ways as 'entropy'? This is not trivial -- serious influential thinkers like Brooks and John Adams from the beginning of the 20th century, many writers before Pynchon's 1960 thunderbolt, and a zillion authors since have made the public aware for years about the dangers of 'disorder' and the 'threat' of the second law and 'too much entropy'. Fiction indeed is fun, but its continual warping of the concept of entropy has resulted in serious individuals being seriously misled. Economics? Specifically, I contacted approximately 12 econ profs about co-authoring an article with me re absurdities in the biggie, Georgescu-Roegen's "Entropy Law and the Economic Process". The response of the 3 who bothered to reply was, essentially, fgeddabout it -- his approach to econ (emphasis on entropy) is deader than dead! (But Rifkin arose!) And who knows how many young students 'find' Geogescu-R. each year and think about it as a possible great discovery, useful for an essay -- and where will they check first? Wikipedia. FrankLambert 23:23, 10 July 2006 (UTC)

Explanation To The Group ( not part of article)
The essence of Clausius’ original words are in the above paragraph. They differ somewhat from the version in the present Wikipedia ‘Entropy’ article, because (as shown below ) my statements use the German of his 1865 paper, cited in an authoritative history “The World of Physical Chemistry” by Keith Laidler (Oxford, 1993, p. 104-105):

“…schlage ich vor, die Grösse S nach dem griechischen Worte ή τροπη [trope], die Verwandlung, die Entropie des Körpers zu nennen. Das Wort Entropie habe ich absichtlich dem Worte Energie möglichst ähnlich gebildet, den die beiden Grössen, welche durch diese Worte benannt werden sollen, sind ihren physikalischen Bedeutungen nach einander so nahe verwandt, dass eine gewisse Gleichartigkeit in der Benennung mir zweckmässig zu sein scheint.”

contributed by: FrankLambert 20:25, 9 July 2006 (UTC)

I propose to name the quantity S the entropy of the system, after the Greek word [trope], the transformation. I have deliberately chosen the word entropy to be as similar as possible to the word energy: the two quantities to be named by these words are so closely related in physical significance that a certain similarity in their names appears to be appropriate.

Good work Frank, I've been looking for this quote for a long time. I'll add it to the article. Thanks:--Sadi Carnot 00:46, 10 July 2006 (UTC)


 * Also, today I was at the sacred library collection at UIC and I read through an original copy of Clausius’ Mechanical Theory of Heat (365 pages) containing his nine memoirs (1850-1865), and thus I added the original 1854 mathematical statement of entropy word-for-word, so there is no confusion as to how this concept first started.--Sadi Carnot 11:12, 11 July 2006 (UTC)

Ice melting - description for photo
To The Group, explanation of advantage to describe illustration better: The illustration in the present Wikipedia “Entropy” is a neat idea, especially with the terrific enlargement possible! The ice and water phases can be very clearly seen. However…! Its present title indeed applies to the photo but it can hardly be called an aid for the naïve reader! Below is a complete description of what lies behind the photo and the phenomenon, perhaps a bit high level for the reader with no background other than the first paragraph above, but about on the level of a reader after the Overview.

Ice melting in a 77 F (298 K) room: - a classic example of heat energy, q, from the warmer room surroundings being ‘transferred’ to the cooler system of ice and water at its constant T of 32 F (273 K), the melting temperature of ice. Thermodynamic System The entropy of the system increases by q/273 K. [q is actually the ΔH for ice, the enthalpy of fusion for 18 grams]. The entropy of the surrounding room decreases less (because the room temperature T is higher, as q/298 K versus the ice-water of q/273 K shows). Then, when the ice has melted and the temperature of the cool water then rises to that of the room (as the room further cools essentially imperceptibly), the sum of the dq/T over the continuous range (“at many increments”) in the initially cool to finally warm (room temperature) water can be found by calculus. The entire miniature ‘universe’ of room surroundings and ice-water-glass system has increased in entropy. Energy has spontaneously become more dispersed and spread out in that ‘universe’ than when the glass of ice and water was introduced and became a 'system' in it. FrankLambert 20:25, 9 July 2006 (UTC)


 * Good contribution Frank. Giving the paragraph a quick skim, it seems to be reasonably accurate.  I’ll add it as a new header section to the article and if anyone what to tweak it from there, the can.  People, from the last archived talk page, keep leaving messages about the ice photo, so maybe this will help?--Sadi Carnot 01:34, 10 July 2006 (UTC)


 * YIPE! Thanks! but this was written as an explanation of the illustration -- and should accompany it as a lead-in for the whole article in explaining the concept of system and surroundings. MUST be at the beginning to try to soften the entree of laypersons, i.e., 'This is going to be a somewhat readable site.' :-) ((Why else would I or anyone use Fahrenheit temperatures!!!!!}}


 * (Thanks to Sadi, I have referred to the excellent diagram in Thermodynamic System and twice more explicitly identified the room as 'surroundings'.) Please put this in a box or similar next to the illustration!! (Don't you see what a layperson, souza, says? 'It's better not to have to refer back...! I KNOW how to teach beginners and laypeople -- and even chemical pros!) FrankLambert 21:32, 10 July 2006 (UTC)


 * Frank, I added a picture of a glass with ice cubes in it and adjusted your paragraph accordingly. Thanks: --Sadi Carnot 11:07, 11 July 2006 (UTC)


 * SORRY! That just doesn't do the needed job -- for a relatively simple totally correct quantitative introduction to entropy change via a sensationally good photo! Placed at the START oif the article WITH the original photo, it does several jobs: aids the beginning chem student to tie in and see the quant reason for entropy maximization in all spontaneous events, catches the interest of the layperson (who will skip by the quant implications, but get a sense of entropy change involving system and surroundings). The explanation MUST be at the article start of WITH that great photo! FrankLambert 18:20, 11 July 2006 (UTC)

Overview
FL suggestion: Paragraph 1
 * A modern view of the second law states that energy of any type spreads out from being localized to becoming dispersed, if it is not constrained. Entropy is extremely important in thermodynamics – and to anyone's understanding of how the world works -- because it accurately measures that dispersal of energy: how much is spread out in a process, or how widely dispersed in space  it becomes, always involving temperature. The explanation of exactly what is happening in the above illustration of a glass of ice and water shows how spontaneous events can be analyzed in quantitative terms.  As you see in this little example, the trend in nature is toward energy becoming evenly distributed, throughout all volumes that it can access, toward a state of equilibrium.
 * Comment: Ummm... I think I prefer what's there already.  I can't remember who contributed it (it wasn't me), but IMO the current first line is particularly good:
 * In a system made up of quantities of matter, its pressure differences, density differences, and temperature differences all tend to equalize over time. The system's entropy, which increases with this process, is a measure of how far the equalization has progressed.
 * IMO the following very simple two lines about the cup of tea then take that on rather simply and naturally. Jheald 17:40, 10 July 2006 (UTC)


 * Of course "In a system made up of..." is a beautifully concise summary of the meaning of entropy to you and to me (ignoring the bit of a problem in precisely vs. broadly defining 'system', especially in the example.) But would we be looking up 'entropy' in Wikipedia? How about the people who would? Who do you think they would be; what do you think would best reach THEM as a starter to explaining simply what entropy is?


 * Don't you see that the "In a system....all tend to equalizee....entropy increases is a measure.." is just plain magic to a non-scientist? "WHY does everything equalize? What is entropy, REALLY? Measuring equalization, whathell does that mean? What's wrong just with "a percentage of equalizing" for a measure of that progress? 50% = half equalized. Good enough for me."


 * What I wrote is WHY the approach has won the texts: (not enough details here; I knew you'd cut 'em but) the basic thrust is 1. WHAT MAKES [systems tend to equalize]? WHY ARE [there energy differences]? HOW CAN [entropy measure 'equalization']?


 * The difference is -- I think -- that I'm trying to explain things to a beginner OPERATIONALLY -- something less abstract than the verbiage that is SO well accepted in our pro circles, but SO hopeless to beginners. (And I restrained myself from writing what you straitlaced old adults would disdain as below WWWWikipedia's reserved dignity:


 * "Light from the hot wire in a light bulb spreads out. The sound from a big stereo does not stay inside a dorm room. Molecules of a gas ..." etc.,etc. Do you see what's common here? They aree all forms of energy -- AND they're all dispersing.....That's the tenor, the level that I believe would fit the needs and wishes of the majority of Wikipedia readers. Why would most of them be so superior to average college frosh in a chem class?


 * Of course, the present photo in the article of the ice in water PLUS its explanation that I wrote below to accompany it -- qual and quant -- is far superior to the cuppa hot water. Please put the explanation with that photo!! FrankLambert 05:08, 11 July 2006 (UTC)

FL suggestion: Paragraph 2
 * Thermodynamic Entropy, unfortunately, has often been misdescribed in the past century as “disorder” or “mixed-upness”. These are non-scientific, imprecisely quantifiable, common language and thus commonly confusing terms that have been used even by many scientists but are now being re-evaluated.  Most modern US chemistry texts, i.e, editions published since 2004, have deleted the old phrase “entropy is disorder” and replaced it with the scientific view of entropy as a measure of energy dispersal/T.  This approach is explained in more detail in the section for beginning chemistry students and others in Section 2, “An Introduction to Entropy Change”.  A different view is presented in the section for beginning physics students and others in Section 3. “The Physicist’s View of Entropy”. ‘Disorder’ appears in other sections at the choice of Wikipedia contributors, not as approved by chemistry professionals. FrankLambert 20:25, 9 July 2006 (UTC)


 * Comment: I find this too much of a campaigning paragraph at so prominent an introductory position. Also, IMO the run of "misdescribed", "non-scientific", "imprecise", "unquantifiable", "confusing" reads rather strident, more like a polemic than the "neutral tone" Wikipedia aspires to. On a broader level, I think it's a mistake to dismiss Feynman and all as simply 'wrong' for using the word disorder.  I'm happy to flag the word as problematic, (and to examine some of those problems in more detail later), but I think it's much happier to indicate that when Feynman and many many older texts use the word, they do so with a particular defined meaning in mind (more mixedupness/more disorder = more microscopic states compatible with the macroscopic description).  The real problem is if people equate orderedness only with the orderedness of the most visible aspect of the system they can actually see (eg creationists looking at increasing order in cells, without accounting in the heat the cells are dissipating to achieve it).   And orderedness can be quite useful in discussing entropy changes -- for example ISTR the orderedness being imposed on water molecules, when discussing trends in the solvation entropies of group I and group II metal ions. Jheald 17:40, 10 July 2006 (UTC).


 * I strongly support Jheald's comment.
 * I would also add that this is a collaborative encyclopedia rather than a book by a single author. Therefore we should try not to force our own description of physics/chemistry as the only one acceptable, even if we really like it. Furthermore, we should not make too many explicit connections between sections, because they might not be respected/noticed by future editors and it will be a mess.
 * Yevgeny Kats 18:14, 10 July 2006 (UTC)


 * First to Yevgeny: You are absolutely right about supporting Jheald's comment -- and also about explicit connections. I am a novice to Wikipedia. But, your implication that my writing is my own description ALONE is corroboration of your failure to investigate or check up on it! It is mine, but it is the present current major description in chemistry. Thus, I'm not pressing MY description AS my description -- it's now the general view in frosh chem, and that is what it will be for years. What's the present gen chem text at Harvard? [It would] Take you 10 minutes to stroll over and find out. Chances are 3 to 1 that it is one that has deleted 'disorder' and follows closely what I have described to you in more detail than most genchem texts because it blends up to phys chem.


 * Then to Jheald: Yeah that second sentence is true but I shouldn't have written it. Over the top. Too strident. So cut it. I found an interesting angle about the Feynman quote. As you know, Feynman has editions that have a few differences. The following was quoted in the Journal of Chemical Education 80, 2003, 145-146, cited from a 1977 edition: Feynman, R. P., et al. The Feynman Lectures on Physics, Vol. 1; Addison-Wesley: C. I. T., 1977, Sect. 46-5, p. 46-7. I have now inserted brackets and a, b,c in that exact quote: “We measure disorder  [a] by the number of ways  [b] that the insides can be arranged so that from the outside it looks the same...entropy [c] measures the disorder." [a]     However, if [b] measures [a] and [c] measures [a], then [b] measures [c] -- i.e., [c] entropy is measured by [b] the number of ways (the number of quantized microstates).  “Disorder” is a needless intermediate between entropy and what it measures! Interrressting:-)


 * The whole deal is that 'disorder' is a dying bad word to thermodynamic entropy, dead already in chemistry. That is IN NO WAY a detraction from the achievements or character of great, noble, clever, wise people who happen to have used it in the past when it was the only game in town!!! But in honesty and good faith to current and future students, it MUST be downplayed. 'Flag it' if you will but make that flag wave mightily! AND make its replacement well known. I clearly had a tough skilled anonymous thermodynamicist on my 'Disorder...' article. He improved it by vigorous challenges but said he could not approve the total deletion because then what could he substitute for 'disorder'? I strengthened my first tentative 'dispersal' ideas specifically for him and outlined what I MIGHT go toward in what later became "Entropy Is Simple, Qualitatively". THEN in the 2nd go-around, he passed me. (For Yevgeny: The substitute -- that is now thoroughly approved by all those text authors -- is described by that umbrella phrase "dispersal of energy...".


 * YES! There are MANY instances in intermediate chemistry (and more in advanced and in research) when one can use a 'quick and dirty' description of some substance/situation/state as 'ordered' or 'disordered' as related to entropy (change) -- BUT the pro (or especially, student) must always be alert as to 'what has happened in leading up to this situation -- energy-wise??' Energy becoming dispersed somehow is the fundamental enabler! FrankLambert 05:08, 11 July 2006 (UTC)

Frank, I see that you don’t like the order/disorder connection to entropy; and from your talk-page comments, I see that you would like to ban it from the world. The problem here is that this is a widely used description; this morning, for example, I am reading Joon Chang Lee’s 2001 Thermal Physics – Entropy and Free Energies book, and it is filled with order/disorder stuff. Thus, knowing that WP is a neutral point of view information presentation forum, we simply have to present concepts as they are, from all perspectives. In summary, my point is that WP is not a place to debate whether something is right or wrong. Thanks: --Sadi Carnot 13:13, 11 July 2006 (UTC)


 * 2001? 2001??!! Thermal Physics??!! My articles that caused the revolution in teaching entropy in General Chemistry were not published in JChemEduc until 2002!  Do you think Lee should have had ESP? How could he have known about my approach? Check the articles in JCE for February and October 2002 (or in the site that I believe you and others on this 'Entropy' labeled as spam! "Disorder -- A Cracked Crutch..." at http://www.entropysite.com/cracked_crutch.html, and "Entropy Is Simple, Qualitatively at http://www.entropysite.com/entropy_is_simple/index.html.  In his next edition, Lee will either have an extensive apologia for his use of 'disorder' in previous editions or he will be left behind in the dust of the old 20th century :-)


 * Sadi, it isn't a question of like or dislike. It is a old problem in aiding students to understand entropy.  None of you have could have had half of the experience I have had with chemistry students, AND with professors who teach them.  I'm not a grad student or under-40 non-teaching-chemistry individual!  The common experience and the common conclusion -- that I urged each of you to check from personal experience with co-students not as bright as you, probably -- is that entropy is the least understood and most feared and hated topic in general chemistry.  You had a year of chemistry, didn't you?  No problem with undertanding what entropy 'really' was?  Could you clearly, without one equation, describe why heating a system increased its entropy, how that was both similar and different than a gas expanding into a vacuum?  As a youngster in gen chem, you understood all that you read a week ago in this thread's Archive 2, inset in "Disorde is DEAD in introducing entropy to students/readers" that I described back there for Yevgeny Kats?


 * But that fear and hate is primarily because of the only summary, brief explanation, used since 1900 has been 'disorder'. It was 'the only game in town', the only (but totally non-scientific) way old profs from the 1920s in thermo and 1960s in gen chem (when it was introduced there) could talk about it, outside of equations.  I've repeatedly described its inaptness.  IT DOESN'T WORK in helping beginners to understand what entropy really is!  I know from long experience that it doesn't work.  (I used it for years with non-science students, and I was far stupider than Lee: I thought it really meant common-language disorder.  Great fun to talk that way (but they were non-science kids;  they didn't have to go on to work with it in science.) When I see such alums of many years ago, I apologize to them for misleading them. And they laugh. They can.)  But a chem student back then or today must USE thermo and entropy. No fooling around.


 * 'Disorder' doesn't give students any idea of what entropy is! Do what I have done: stand outside a classroom where you're unknown shortly or long after entropy has been presented in that class and strike up a conversation with a student hanging around.  (And the fun is, if you're obviously not a student, 1 then 2 then maybe 4-5 drift closer :-))  Ask "Just for my own curiosity -- no quiz -- what did you learn about entropy, what do you think about entropy?  What is it really?"  After the usual repeatedly scatological answer, all that usually comes out is a weak variation of disorder, disorder, disorder.  No sense of general understanding of what entropy is all about, or why.


 * ENTROPY IS A SIMPLE CONCEPT when it is developed correctly. Its power and universality becomes obvious.  That's why 'disorder' was deleted from gen chem texts!  Their author or one of the authors has each struggled to teach entropy to first-year students.  My approach WORKS.  It has been taught to at least 100,000 students in the past two years. (Most texts of "my 15" didn't change until 2005.)


 * The debate is over in general chemistry textbooks. It has not BEEN a debate in most physical chemistry texts published even in the past 5-6 years (except fot Atkins, who has just changed to my approach.) WP should certainly reflect current views in teaching thermodynamics in chemistry -- and question more strongly the view of entropy as 'disorder' because its demise is inevitable and WP should make readers aware of the immediate future.  The unending arguments between WP people from the beginning of the Talk:Entropy/Archive 1 demonstrate conclusively what a mess 'disorder' itself is -- and the more recent arguments among you WP participants certainly underscore its vacuity! FrankLambert 00:33, 12 July 2006 (UTC)

I can’t believe you’re still trying to talk junk to me? It occurs above twice and on seperate talk pages as well: here and here. In Wikipedia terminology, these are called person attacks. Before you go around making any more of these, you might want to read the section "no personal attacks" which states: Do not make personal attacks anywhere in Wikipedia. Comment on content, not on the contributor. In any event, in addition to what I’ve just posted below, here and here, in regards to you thinking that you know about entropy even though, as you state, you have never read any of Clausius’ work (which in itself is very humorous); from Anderson’s 2005 Thermodynamics of Natural Systems (textbook), we find:

Virtually since the beginning, a popular viewpoint has been to see entropy as a measure of disorder. Helmholtz used the word “Unordnung” (disorder) in 1882.

Lastly, in regards to your presumption: “You had a year of chemistry, didn't you?”; for the record, in regards to knowledge of entropy, one chemical engineer (me) is more knowledgeable than any three chemists (you) put together. Thank-you for your attempt at trying to belittle me. Adios: --Sadi Carnot 05:17, 13 July 2006 (UTC)


 * I apologize for any personal attacks, Sadi, and have deleted the first two instances that you referred to above. In the others, I am in no way attacking you. I am urging you to consider/confront the problem that 'disorder' poses to the beginning student. You and the information specialists in the Talk:Entropy page undoubtedly were very bright beginners and 'went with the equations' so that 'entropy is 'disorder' was a trivial definition that didn't bother you. Most students however, that I have ever questioned -- and the two research papers studying student understanding and attitude toward entropy (Turkey and UK) -- come to the conclusion that students are confused by that definition, uncertain of having any understanding of entropy. (And in general hate it.)


 * Thus, please re-read the paragraph about 5-6 paragraphs above this -- There, I'm not sneering at you that you had only a year of chemistry, as taking the sentence out of context seems to imply. Instead (as you will see by re-reading), I am pleading, by repeated questions, that you think back to your first year of chemistry and your -- but especially their (the less able students than you) -- first experience with entropy. If their unhappy experience and distaste for entropy could be avoided and the understanding of the next groups of beginners improved from now on, don't you think it should be? And, as I show from current textbook citations (at the end of your long quotation for Clausius below), I am not talking 'junk' to you, not urging the deletion of 'disorder' just because of a 'like' or 'dislike'. I am patiently trying to aid you to see that 'disorder' need no longer be the definition of entropy, that there is a far better, simpler, more nearly correct approach -- that has already been adopted by the majority of general chemistry texts and two physical chemistry texts.  WP has an opportunity to join the 21st century view of entropy, but you and two others appear unwilling to consider it seriously. FrankLambert 23:40, 13 July 2006 (UTC)

Page two of present article printout
FL proposal:
 * The entropy of a thermodynamic system can be interpreted in two distinct, but compatible, ways:


 * • From a macroscopic perspective (i.e. examining a system only by what we can see and measure by properties like volume and pressure and temperature) in classical thermodynamics the entropy is interpreted simply as a state function of a thermodynamic system: that is, a property depending only on the current state of the system, independent of how that state came to be achieved. The state function has the important property that, when multiplied by a reference temperature, it can be understood as a measure of the amount of energy in a physical system that cannot be used to do thermodynamic work.


 * FL comment: This is part of what is probably the dumbest artificial complexity in science! You have seen or will see somewhere that “entropy is unavailable energy” or “waste energy” from a chem. reaction.. The statement is not complex; it simply doesn't try to be clear. It’s obscure and not true -- and also true!  Not true: "The energy in any iron pan at room temperature is NOT instantly available to start melting an ice cube."  True: "However, if it transfers any energy to the ice cube, the pan no longer can exist in the same energy state that it was at room temperature!" "The terrific amount of hot gas coming out of a car’s exhaust is “waste energy”." Not true, in the sense you could pipe to radiators in a house and warm the whole house (in time). But it is true in the sense that it is ‘waste energy’-- so far as the combustion reaction of gasoline with oxygen is concerned; it isn’t available at the original high temperature of the combustion reaction.


 * Entropy is a measure of the “unavailable” energy in a substance only because it is an exact measure of the amount of energy that the substance needs to exist at equilibrium with the surroundings at a particular temperature! THIS is the powerful concept behind the above and what follows by Jheald. Why isn't it presented to a student first? FrankLambert 21:21, 11 July 2006 (UTC)


 * For me, the current next two lines are the most important, because IMO they give the clarity needed to interpret the previous lines into something explicit:
 * More precisely, in any process where the system gives up energy ΔE, and its entropy falls by ΔS, a quantity at least TR ΔS of that energy must be given up to the system's surroundings as unusable heat (TR is the temperature of the system's external surroundings). Otherwise the process will not go forward.
 * (See also the discussion at Second_law_of_thermodynamics and exergy).
 * Yes, strictly it assumes a model of system + surroundings, with the surroundings being considered as an unlimited temperature and pressure reservoir, with an identifiable reference temperature and pressure TR and PR. But I do think the idea of "unavailable energy" is hugely important, because (i) it's where the entropy idea came from; and (ii) it's one way to define entropy in purely macroscopic terms, and much better for motivating classical entropy than saying "it's just a state function" .  I like that we can give some motivation for entropy in classical terms, before we present the microscopic picture which encompasses and explains it. Jheald 17:40, 10 July 2006 (UTC).


 * Jheald's statements are totally good thermo, and almost totally not understandable by a first-year student IMHO. (And many third-year? I don't know.) That's my major beef, throughout this beginning of "Entropy". Express it in 'thermo speak' only if you have first explained it operationally or simply so most -- or at least most average -- chemistry students can understand it. (The challenge I've given to some profs, not anyone on this 'case': If you can't do that, do you really understand it yourself?! )FrankLambert 21:21, 11 July 2006 (UTC)

FL proposal:
 * • From a microscopic perspective (i.e., from examining what the molecules or other little particles are doing in asystem) in statistical thermodynamics the entropy is envisioned as a measure of the number of microscopic configurations that are capable of yielding the observed macroscopic description of the thermodynamic system. Each configuration represents one arrangement of all the energies of all the molecules of a system on energies levels at one instant, a quantum microstate.. In the next instant, one collision of a molecule with another is enough to change the microstate into another accessible microstate. The more such microstates, the greater is the entropy of a system. It can be shown that this definition of entropy, Boltzmann's postulate, reproduces all of the properties of the entropy of classical thermodynamics.
 * Comment: not sure about (i) taking out that when older books use "mixedupness" and "disorder", this is what they mean; (ii) playing up the collisions so much; even making them sound like part of Boltzmann's postulate. After all, one description of the system is that it is just staying in one state, evolving deterministically according to the the Schroedinger equation.  The "quantum jumps", which erode information in the H-theorem, really come in only when we demand to shoehorn reality into a model of different susbsytems, constrained to go on remaining statisticially independent. This is a modelling decision, which may impact how what we consider to be the entropy evolves.  But there can be an entropy (an uncertainty), whether or not we choose to model it as increasing through quantum jumps. Jheald 17:40, 10 July 2006 (UTC).

FL proposal:
 * An important law of physics and chemistry, the second law of thermodynamics, that we have already informally defined as ‘energy spreading out or dispersing, if it is not hindered – measured as an entropy increase’, we can see in formal terms as the total entropy of any isolated thermodynamic system tends to increase over time, approaching a maximum value. (Energy spreads out as much as it can.) Unlike almost all other laws of physics, this associates thermodynamics with a definite arrow of time. FrankLambert 20:25, 9 July 2006 (UTC)
 * Comment: Hmm. Not sure. For myself, I think the mention of the 2nd law stands better by itself, just as a property of entropy, how ever you want to think about entropy, without again bringing in the energy spreading out or dispersing. On balance I think the article would be leaner and cleaner without forcing this picture of entropy on this paragraph.


 * (@ Frank: I'm honestly not trying to take up the role of advocatus diaboli against any and all proposed change. It's just that there were things that made me feel uncomfortable, and I'd be happier to see them further discussed.  Hope that's okay with you.  All best, Jheald 17:40, 10 July 2006 (UTC))


 * I'm just an ignorant layman trying to get my head round this, but as an introduction I think it's helpful to focus on the energy spread, then subsequently explain the other angles. This is partly because it's easier not to have to refer back, and partly because as far as I can tell the second law has very restricted application to information entropy. This is important as a common creationist theme is that the second law means that a Creator is required for an increase in "information". Sorry to introduce that side, but I'm coming at this from trying to find out enough to effectively counter such ideas. ...dave souza, talk 19:28, 10 July 2006 (UTC)

What needs to be added for Chemists ?
WikiProject_Chemistry currently rates this article as "needs more chemistry to go with the physics" (note: rating is not necessarily that recent).

In progress, I think we're already discussing issues about the appropriate tone to make a friendlier article for P Chem students. (And, what specifically in the article might make it seem less friendly, or even alien to P Chem students).

But what *topics* should Physical Chemistry students expect to find presented here, that aren't already (and/or in breakout articles from here) ?

eg: ...
 * Standard entropies (=> molar quantities, measured at stp, etc).
 * Relationship with ΔG°, spontaneous and non-spontaneous reactions etc.
 * Relationship with Equilibrium constants.
 * Frequent assumption of more-or-less independence of ΔS with temperature.
 * Trends in ΔS in chemical groups for particular sorts of reactions (eg ion solvation ...)
 * Entropy effects in eg boiling point elevation, freezing point depression, ...

Actually, I suspect very little of that on this page, which is mostly signposts to more detailed articles; but perhaps more detail in an Entropy in Chemistry page, or handed off to Chemical Thermodynamics; or in individual relevant pages.

Part of the problem is that (IMO) Wikipedia needs a big push in the whole subject area of Physical Chemistry. The whole P Chem subject area seems a lot less developed, so (as a comparative outsider) I find it hard to find out what needs the Entropy article needs to supply.

Hence this talk subject to try to get discussion going. (And a plea at WP:Project Chemistry for an actively managed initiative to try to push quality in the whole field). Jheald 19:35, 10 July 2006 (UTC).

Entropy is perhaps the most difficult topic that chemistry students ever meet. In fact there are now places, regretably, that now no longer teach it, at least to all students. I am retired now, so I am no longer teaching Physical Chemistry and the publishers are no longer sending me copies of the latest text books. However before I retired I saw the change that Frank talks about, although I did not realise it came from him. I had started to concentrate on energy dispersal rather than disorder. For those chemistry students who are still taught about entropy, this article is not much help. It is way beyond what is in their text books and it really is placing more weight on how physicists see the subject. There is a general problem here with all articles that cover topics in both physics and chemistry. In some areas it is like entropy - one article but not clearly satisfying both chemists and physicists. In other areas, particularly in the areas of molecular physics, chemical physics, quantum chemistry, computaitonal chemistry etc., I keep coming across articles that have a major overlap with other articles - one written by chemists and linking to other chemistry articles, and one written by physicists and linking to physics articles. We need to sort this out. I am not sure how. Maybe we do need different articles. Maybe we need an article on chemical entropy or entropy in chemistry. Better, I think, would be to make this article fairly simple and link to separate more complex articles on entropy in chemistry and entropy in physics. --Bduke 23:57, 11 July 2006 (UTC)

-- One possibility might to have a separate article Thermodynamic entropy (Which currently redirect here) that is a gentle introduction to entropy as physical chemists use it. This article can then be the broad overview article that provides short introductions to all of the other entropy articles. We currently have Entropy (thermodynamic views), Entropy (statistical views), Entropy in thermodynamics and information theory, Information entropy and History of entropy, along with many other related articles in the entropy category. Nonsuch 00:13, 12 July 2006 (UTC)

Disorder at Harvard
Frank is trying to convince us that since some chemistry textbooks now avoid the use of the word "disorder" following his advice, this description is dead and should not be mentioned in Wikipedia. (Instead he suggests to use the vague concept "energy dispersal" that I still cannot understand what its exact definition is). He writes above that I should check what they teach in the Chemistry Department at Harvard. So I took the challenge, and what do I find in the lecture notes of the course "Chemistry 60: Foundations of Physical Chemistry"? It's online: Lecture 8 p. 11: "Entropy S is a quantitative measure of disorder" :) Yevgeny Kats 14:34, 11 July 2006 (UTC)


 * Yes, I just pointed this fact out above, in the Talk:Entropy section, before you put this comment here.[[Image:Smiley.svg|20px|]]--Sadi Carnot 16:43, 11 July 2006 (UTC)


 * Because Yevgeny did not glance at the peer-reviewed articles that I cited on 2/3 July, I carefully summarized them for him in a page and a half on 4 July (under "Disorder is DEAD..."). Now, as shown by the foregoing, I deeply wish that he had read what I wrote especially for him, above in this thread on 05:08 11 July, namely:


 * "I'm not pressing MY description AS my description -- it's now the general view in frosh chem, and that is what it will be for years. What's the present gen chem text at Harvard? It would Take you 10 minutes to stroll over and find out. Chances are 3 to 1 that it is one that has deleted 'disorder' and follows closely what I have described to you in more detail than most genchem texts because it blends up to phys chem."


 * Yevgeny, my remarkable success in changing more than the majority of general chemisty texts does not mean that a phys chem lecturer at Harvard (you were not citing a text, but a lecture) 'has seen the light'! I asked simply that you 'stroll over and and find out' 'the present gen chem text' in the course that was "Chem B" so many years ago when I took it, now probably "2" or "1B".


 * My point is simple, but substantive: Unless you have evidence to the contrary, the major Internet hits on "Entropy" in WK will be beginners or laypersons. The problem with the article as it stands is that few of these individuals needing aid will read or further investigate it beyond the first paragraph or two because it is not 'user-friendly' to that group. I would assume that WK does not, unfortunately because it would be costly, collect data on 'hits' versus 'visits/readers' to individual articles like "Entropy" nor the time they spend on an article. My sites had some 510,000 visits last year from over 2.2 million hits. They are readable by all levels. A comparable figure for "Entropy", due to its limited value to beginners, may well be 20,000,000 or more hits, but my not-totally-uneducated guess would be that there would be less than a million visits. Whatever the exact figures, it is probably that an enormous number of students and laypersons wanting information and guidance will be ill-served.


 * The changes that I have detailed are NOT to make "Entropy" the low-level intro that constitutes much of my sites, but rather just to speak in somewhat less pedantic, less frightening-to-beginners thermo language in the introductory portions of the site. Yes, I was overly strident in a couple of places. Yevgeny and Jheald are right. But the general thrust as well as most of the details of what I submitted constitute a significant improvement to the beginning of the article -- without disrupting any presentation of complex details later in any language you may feel necessary.


 * Change in viewing entropy as 'disorder' is not "coming". It is here in most general chemistry texts today -- and will be 'general throughout science in a generation'! My approach is that simple yet fundamental. (Pin your apologies to my headstone :-) FrankLambert 17:27, 11 July 2006 (UTC)

Frank, I feel that your intentions are well-minded; but you need to loosen up a bit. When you go around tooting that “disorder is dead” and “energy dispersal is in”, what you are doing is akin to censorship. From my talk page, you state that you have never dug into the history of Clausius (1850-1865), but that your interest peeked with the papers of Boltzmann (1872) and Kelvin (1875), below are your words:


 * “I didn't respond about 'good books in the origins of entropy' before Clausius, because my main historical delving was in Boltzmann -- although it WAS the paper of Kelvin about the 'dissipation of energy' that really got me thinking "why didn't Clausius talk about that...wasn't that really what his q was doing in every case of a spontaneous process??' And from that in a year or so (!) came my conclusion that entropy WAS really all about energy dispersal PLUS Clausius brilliant idea that [I don't know if he ever said it this way, but that's why it's so great] dividing the energy involved by T gives you an idea of the intensity/concentration of the energy in any system.”

Well, to contradict you, I do know how he said it. Over the last several days, I have been down at the UIC library reading an original copy of Clausius famous 1865 book Mechanical Theory of Heat, which contains his nine papers between the years 1850-1865, upon which the foundation of entropy is built. In his 1862 paper, he states the following relation:


 * $$\int \frac {dQ} {T} \ = -N$$

where:


 * dQ = an element of the same, whereby any heat withdrawn from the body is to be considered as an imparted negative quantity of heat. The integral in the second equation is extended over the whole quantity Q.
 * T = Absolute temperature.
 * N = the equivalence-value of all the uncompensated transformations involved in a cyclical process.

Clausius then goes on to discuss the underlying nature of the concept of “equivalence-value”, i.e. what he labels as entropy in the following two years. He then discusses how a working body of gas comprised of individual molecules configured into very specific arrangements, i.e. “order”, is changed through “compensations” as it progresses through a complete Carnot cycle; something which Carnot himself did not take into account.

First, he speaks of the change in the arrangements of the molecules of the body not being a reversible phenomenon as the body moves from one state to the next, and in doing so overcomes resistances which are proportional to the absolute temperature.

Clausius then states: “when heat performs work, these processes always admit of being reduced to the alteration in some way or another of the arrangement of the constitute parts of the body. For instance, when bodies are expanded by heat, their molecules being thus separated from each other: in this case the mutual attractions of the molecules on the other one had, and external opposing forces on the other, in so far as any are in operation, have to be overcome.” Hence, we see that in 1862, before entropy was even named, the founder of the concept of entropy is speaking about arrangements of the atoms and molecules of the constituent body and how these arrangements are changed, via uncompensated transformations, as they progress through a cycle. As we see, entropy in its essential nature, is built on the concept of the changes in the ordering of atoms and molecules of the working body. The opposite of order is disorder. This is a core perspective in the concept of entropy; and it is not dead as you seem to think. Just a friendly note: --Sadi Carnot 02:43, 12 July 2006 (UTC)

Entropy as defined by Clausius in 1862
To elaborate further on the preceding discussions, I particularly do not like individuals who purposely strive to alter historical frameworks of concept, in such a manner as to substitute their own personal contrivances for the original. Owing to this conviction, today I was again down at the sacred copies room at the UIC library typing up, word-for-word, the original formulation of entropy, as it was intended to be stated. The entire framework of entropy is built on some 365 pages worth of logical argument presented in nine memoirs over the course of 15 years, from 1850 to 1865. Below are the main points of the way entropy was presented to the world in 1862-65 (starting from pg. 218 of Clausius' Mechanical Theory of Heat [the third page of the sixth memoir]):

(skipping a few paragraphs; Clausius then states the following law (as he calls it)):

(skipping a paragraph)

(skipping about 20 pages)

(Then starting from page 354 of the ninth memoir is where he assigns the symbol S and gives it the name “entropy”)

(Then after a page of derivations, which includes a symbol assignment of disgregation, we then arrive back at the following equation)

(Then, in grand finale of this equation-packed magnificent book, we arrive at his famous last paragraph on the last page [pg. 365] of ninth memoir, first presented to the public as sourced below*)


 * (Ninth memoir): Read at the Philosophical Society of Zurich on the 24th of April, 1865, published in the Vierteljahrsschrift of this society, Bd. x. S. 1.; Pogg. Ann. July, 1865, Bd. cxxv. S. 353; Journ. de Liouville, 2e ser. t. x. p. 361.

So there you have it. I hope this gets us all on the same page so that there is no more talk-page bickering regarding fictitious concepts that were never presented in the words of Clausius. Adios: --Sadi Carnot 04:23, 13 July 2006 (UTC)

And now to 2006!

 * Thanks so much for bringing us up to speed to 1865, Sadi. But now, it is 2006.  Should we not be concerned about how modern scientists and texts describe entropy change, now that we have the third law, statistical and quantum mechanics, and an intimate understanding of molecular behavior?  Here from textbooks on my shelves are a few quotations that, together, certainly are significant in 2006 and 2007 and on, even perhaps to 2065 ! :


 * From the 2nd or 3rd best-selling text for General Chemistry, Silberberg (‘Chemistry’, 4th edition, McGraw-Hill, 2006), p. xviii: “Chapter 20 has been completely rewritten to reflect a new approach to the coverage of entropy. The vague notion of “disorder” (with analogies to macroscopic systems) has been replaced with the idea that entropy is related to the dispersal of a system’s energy and the freedom of motion of its particles.”


 * From the 2nd edition of the text whose previous edition was the most successful 1st edition-seller in many years, Moore, Stanitski, and Jurs (‘Chemistry, The Molecular Science’,Thompson, 2005), p. xiii-xiv: “Specifically we have made these changes from the first edition: … Revised Chapters 14 and 18 to more clearly present entropy as dispersal of energy (see Lambert, F. L. J. Chem. Educ. 1999, 76, 1385; 2002, 79, 187.)”


 * From the 4th edition of Brady and Senese (‘Chemistry, Matter and Its Changes’, Wiley, 2003), p. v: “Chapter-by-chapter changes” …In Chapter 14 we discuss spontaneous mixing as a tendency toward more probable states rather than a tendency toward disorder, in preparation for an improved treatment of entropy in Chapter 20.” …”We have changed our approach to presenting Thermodynamics (Chapter 20). This chapter now explains entropy as a measure of the number of equivalent ways to spread energy through a system…”


 * From the 8th edition of the long-accepted Ebbing and Gammon (‘General Chemistry, Houghton Mifflin, 2005), p. xxiv: “Revision of Material on Thermodynamics: We have completely revised all of the thermodynamics data used in the book, making sure that it is accurate and up-to-date. Also, the discussion of entropy in Chapter 19 was rewritten to present entropy as a measure of the dispersal of energy.”


 * Twelve other chemistry texts have completely deleted ‘disorder’ (or in three cases use it only as a bridge to the past) and adopted the dispersal of energy as an approach to understanding entropy change. They are listed at  “December 2005” on  http://www.entropysite.com/#whatsnew ). There will be a chemistry text or two published this year and perhaps next that do not delete ‘disorder’ but this is to be expected.  It usually takes a generation for a concept to fade away and be replaced.  (It has been only four years since my articles were published and this major shift in understanding entropy change has occurred.)  The point is that the dispersal of energy as spelled out in detail in so many aspects in this Talk:Entropy thread is already a mainstream way of describing entropy change to beginning students in chemistry – and to laypersons. . . . . . FrankLambert 03:53, 14 July 2006 (UTC)


 * Perhaps a fresh viewpoint might contribute to resolving this issue. The main issue of disagreements in this discussion seem to be how Clausius' original definition was suitable for the times, but the current view of Entropy is moving very much away from any descriptions involving disorder.  This current view is being reflected in both classrooms and textbooks, with the latter being an excellent resource for any confusion as to the terminology that the Entropy article should take in Wikipedia. References should be given to the sources that have depracated disorder in Entropy descriptions.  As of 2006, Prentice-Hall's General Chemistry 10th Edition also makes no use of disorder, focusing on the extent of energy distribution due to the combined effects of translational, vibrational, and rotational motional energies of the thermodynamic system at any given microstate. Physical Chemist 04:46, 17 July 2006 (UTC)


 * " but the current view of Entropy is moving very much away from any descriptions involving disorder. ". That's simple not true in general. Certainly, evidence has been advanced that describing entropy as 'disorder' should he handled with care, and that introductory physical chemistry textbooks are avoiding the use of the word. And certainly there are some scholars who vigorously oppose any mention of 'disorder' at all. But I don't see any move away from 'disorder' and similar descriptions in the wider scientific community. Nor even, broadly, among physical chemists. Nonsuch 07:30, 17 July 2006 (UTC)


 * But the point that is being made is that disorder is just not right, and never was right. It was a poor analogy to try and put statistical mechanics into general chemistry texts (abd some physics texts at that) that got out of control.  The energy quanta of a system does become distributed statistically over a wider range of possible vibrations, translations and rotations as the entropy increases; and the second law says this always happens in the universe for an irreversible process; but what does that have to do with being disordered? Admitedly, if you had a non-Boltzmann distribution it would become Boltzmann, but does that really imply that the Boltzmann distribution is "most disordered"?  What does that even mean? I would think it means "most statistically distributed"--i.e., standard normal (if you include direction)--but I'm not convinced that means "disordered." Olin 13:26, 17 July 2006 (UTC)


 * I have no wish to restart the endless 'disorder' or 'dispersal of energy' or 'mixupness' or whatever debate. At this point, I'm simple poiting out that there are differing POV on the issue, which therefore need to be addressed by this article on entropy. Nonsuch 15:24, 17 July 2006 (UTC)


 * This appears to be a genuinely positive step forward. Why don't we each try to write a substitute for the second paragraph of "Overview" and then see what compromise can be reached -- although probably not total agreement with/of either of our opposing views? How about starting an 'Overview - 2nd paragraph' below?  FrankLambert 18:15, 17 July 2006 (UTC)


 * I would agree that the second paragraph you are referring to has some changes that need to be made. Reading it does not seem to induce any extra information, instead focusing on the 1.) Suspect nature of the definition, 2.) The difficulty in using the definition in this manner, 3.) Then still trying to define it in this respect.  I suggest a complete deletion of this paragraph so that the overview goes from the first paragraph directly into the overview section with the two interpretations of entropy. Physical Chemist 18:52, 17 July 2006 (UTC)


 * I agree with Physical Chemist that this paragraph in its current form does not contain much useful information, and I think it would be a good idea to delete it or move it towards the end of the article. I disagree with Frank's suggestion of using the concept of "energy dispersal" in defining entropy, as I already explained several times. Yevgeny Kats 21:41, 17 July 2006 (UTC)


 * Kats -- at Harvard


 * Back on 11 July, I urged Yevgeny (who is a grad student in physics research at Harvard) just to stroll over to the chem building and find what text Harvard first-year chemistry students used in 2005-2006, and thus what they are taught about entropy -- disagreeing as he does with "Frank's suggestion" of "energy dispersal". He hasn't strolled. So, from 3006 miles away, I walked to check on Chem 7 in which thermo and entropy were introduced in the Spring semester to 'Harvards'. Professor Anderson used the text, "General Chemistry" by Petrucci, Harwood and Herring (10th edition, so those authors have been around the track plenty of times)


 * (OF COURSE, the bold italics in the following were inserted by me, by damn!) On p. xxviii of the Preface the authors state "In Chapter 20 (Thermodynamics) the concept of entropy is introduced in a new way...". Then, on p. 784, in 20-2 "The Concept of Entropy", the conclusion of the paragraphs accompanying the usual two-bulb gas expansion illustration is "The tendency is for the 'energy of the system to be spread out' over a larger number of energy levels."  The next paragraph discusses gas mixing and the next to last sentence is "Again, each expanded gas has more translational energy levels available to its molecules -- the energy of the system has spread out ".  (The word 'disorder' does not appear in the chapter!)


 * Just as I patiently explained, specifically for Yevgeny, in a full page on 4 July (Archive2, "Disorder is DEAD..." the power of the simple concept of entropy increase as the dispersal of molecular energy over 3-D space is shown by its seamless connection with energy levels (that Petrucci, Harwood and Herring make immediately). The easily visualizable 3-D event and idea of energy spreading out is readily associated (in their Figure 20-3) with the quant mechanics of energy levels and molec energy distribution -- denser levels in volume incrase, more access to higher levels in a temp increase.


 * It ain't just "Frank's suggestion", Yevgeny! Those other 14-15 texts referred to above are being and will be used around the world. Even at old Harvard.  FrankLambert 18:07, 18 July 2006 (UTC)

Article focus
What is (or should be) the focus of this article? Much of the recent discussion has focused on how particular communities construe the word, either presently, or in the past. IMHO, this article, which is simple entitled 'entropy', should give a concise definition, a short introduction to the concept, a brief history, and a discussion of various ways that entropy has been used in different contexts, and at least a listing of related concepts, special cases and generalizations, with suitable crosslinking to more specialized articles. Discuss. Nonsuch 07:30, 17 July 2006 (UTC)


 * I apologize to nonsuch, Jheald, and Carnot for my unseemly expression of frustration at making no progress in at least some compromise that would result in some change in the Entropy article. They are experts in their specialties. I am an expert in teaching the basics of thermodynamic entropy. My approach that has been remarkably rapidly and widely accepted in general chemistry texts since my 2002 articles (as it was implicit in several physical chem texts before 2002-3). However, it is not generally known outside of chemistry as of now.


 * That may well change toward the end of this year. Harvey Leff, theoretical physicist and world authority on Maxwell's demon, published an article in 1996 about the spreading and sharing of energy that soundly supported my qualitative concept. It is just now coming to the attention of physicists in that he was invited to present his latest ideas to an AAAS Theo Physics group in San Diego in June and that paper should appear in Foundations of Physics [I think I have the correct title] in a few months. Changes in old scientific concepts do not normally occur in a few years. The astounding rate of change in chemistry of focusing on the dispersing of energy in viewing entropy may not be paralleled in physics, but the change in chemistry certainly should not be ignored in Wikipedia.


 * Entropy was defined and used in thermodynamics from the invention of the word by Clausius. Those using the word were physicists, stoutly joined by chemists in the 20th century. Thermodynamic entropy was and has been the only use of the term entropy in chemistry and physics until 1948. Thermodynamic entropy still is the sole meaning of 'entropy' in the hundreds of chemistry textbooks at all levels but a handful or less of advanced texts applicable to both chem and physics. There is no compelling reason that the theme throughout the article "Entropy" be anything but thermodynamic entropy -- because at the outset, it is clearly stated where separate articles discussing other uses of entropy can be found. FrankLambert 14:22, 17 July 2006 (UTC)


 * The problem is that the introduction talks about thermodynamic entropy, and in particular the Clausius definition, but much of the rest of the article talks about entropy in more general terms. I'm advocating that either we need a separate "Thermodynamic entropy" article, or a separate "Entropy (Overview)" article. The reality is that the concept of entropy is far more widely used that just thermodynamics. The overview article is probable the right place to discuss the issue of "What is entropy, anyways?", but given the widely varying points of view, probable not in the introduction. Nonsuch 23:58, 17 July 2006 (UTC)


 * I agree with Nonsuch. Entropy has two equally important aspects: (A) as a state function in thermodynamics; (B) as counting the number of microstates in statistical mechanics. Currently, the introduction presents only one particular property related to (A), and nothing about (B). I don't think we should write several separate articles. I think we should include everything is this article since we're talking about the same physical quantity. Yevgeny Kats 00:11, 18 July 2006 (UTC)

"Overview" in WP Entropy article. Revision of the present 2nd paragraph
As a first draft:

"Entropy has been described in texts, dictionaries, and encyclopedias for over a century as "a measure of the disorder of a thermodynamic system" or "how mixed-up the system is". This is unfortunate because "disorder" and "mixed-upness" are not quantifiable scientific terms in themselves. A modern description of entropy that has appeared in most US general chemistry texts as of 2006 is readily understandable and directly related to quantitative measurement It is "Entropy is a measure of the dispersal of energy (in chemistry, most often the motional energy of molecules): how much energy is spread out in a process, as in 'thermal entropy' and/or how widely spread out it becomes, as in 'positional entropy', both at a specific temperature." (Information theory deals with the quantitation of 'disorder' and 'mixedup-ness'. See the links to articles in its section that follows.)" FrankLambert 18:48, 17 July 2006 (UTC)


 * This proposed paragraph does not satisfy NPOV. Not even close. Nonsuch 23:39, 17 July 2006 (UTC)


 * This is YOUR POV, Nonsuch. Using NPOV criteria : Is the first sentence unverifiable in any way? The second sentence, is the word 'disorder' a quantifiable scientific term PER SE -- without reference to its unusual use in information theory? (Do you want to drop the adjective "unfortunate"? Fine, let's talk about it.) Please, would you write your paragraph? Must we not both recognize that the first sentence is an 'establishing' sentence to bring all readers to see where we are? FrankLambert

Assessment for WP:Chem
In reply to the comments of Jheald above, I have reassessed the article for WikiProject Chemistry as "Start". A lot of specific chemical information (eg, measurement techniques) can go into Standard molar entropy or into Gibbs' free energy, as these are the quantities which chemists actually use, but there needs to be enough of a "taster" here so that chemists will know to look elsewhere for the details. Gibbs' free energy is not mentioned by name, although the concept is used in the article! Similarly, there is no mention of the Third law of thermodynamics, which surely has a place in a general discussion of entropy...

I would like to see at least one example of a chemical system in the article: I usually use the reaction between chalk and hydrochloric acid, as the evolution of a gas and the dissolution of a solid always lead to an increase in entropy. As the article stands, I do not see how a reader can get a grasp as to what entropy actually is, beyond the fact that it happens to be equal to dqrev/dT! The example of the Ellingham diagram also works well with French students: entropy as an approximation to d(&Delta;G)/dT in the absence of phase changes. I am mystified by the current choice of example: the article presents entropy as the energy which is not available to perform work, but chooses an example where no work is done at all! I'm teaching "Basic Physics for Environmental Scientists" this summer ("basic" includes such joys as damped and forced oscillators, Reynold's number and Fick's Laws, so I'm glad I don't have to teach "advanced"!), and I will almost certainly use the example of a steam pump to illustrate entropy. I will use the example of melting ice to check if they have understood what a phase equilibrium is ("OK, so it's in equilibrium, so what is &Delta;G? So if &Delta;G is zero, what is &Delta;S?"). The use of the entropy unit in American publications should also be mentioned.

On a more general level, care needs to be taking with the mathematics. The "d" of a complete differential is always in upright type, latin letters denoting physical quantities (q, T) are always in italics. Entropy is a state function, not a differential, and so is equal to dqrev/dT, not dQ/T as stated in the article and earlier on this talk page (either lower or upper case "Q" may be used for heat, I'm not complaining about that). As we have the correct Greek spelling of trope, this should be included.

Finally, the definitions seem to be rather too based on a historical presentation, even if I cannot fault the quality of the history. The section "Thermodynamic definition" is six paragraphs long, but stops at 1903! IMHO, the force of Clausius and Boltzmann is that their ideas are still taught a century and a half later in virtually the same terms as they themselves used: I feel that we should honour them by teaching these ideas as physical facts and not as historical facts!

An appropriate response to all this would be sofixit, but I'm not going to dive into the article itself without some feedback on my views (feedback can be good, just ask Jimi Hendrix). All the more so as I remark that the article is dissipating quite a lot of energy as heat which, as we all know, can only be to the detriment of useful work :) Physchim62 (talk) 18:16, 18 July 2006 (UTC)


 * Broadly, I concur with your suggestions. My preference would be to relegate most of the (very interesting) historical discussion to the specialized history of entropy article, and, as you say, teach the facts as currently understood.
 * As an aside, does anyone actually use 'entropy unit'? Personally, I have never run across the term in the wild (But I don't read a lot of experimental thermodynamics).
 * Also, I would still appreciate feedback or comments (Anyone?) on what the focus of the article is or should be. If this article is strictly about thermodynamic entropy, then we can remove 3 or 4 sections and write a really good, focused introductory article. But then we need a new, broad overview article.Nonsuch 18:40, 18 July 2006 (UTC)


 * I agree with Physchim62 that it's a good idea to remove all the historical discussion from the main text (only the History section will talk about history, or maybe a separate article). Free energy and the third law should definitely be mentioned. S = dQ/dT is wrong! The correct statement is that the change (or difference) in entropy is dS = dQ/T. Actually, dQ/dT is heat capacity. Yevgeny Kats 22:42, 18 July 2006 (UTC)
 * I have to agree with Yevgeny Kats on differentials, although that doesn't change the fact that the current version of the article is wrong! Entropy units are used with calorie-based systems, and it is quite common for European readers to wonder what they are. The article as it stands is exemplary for having mostly taken the effort to include equivalent units, but the omission of e.u. seemed quite striking.
 * As for the focus of the article, I think it should mainly deal with entropy as used in physics and chemistry, with references to other uses. "Entropy as used in physics and chemistry" includes both the "classical thermodynamic" definition and the "statistical" definition, which chemists consider as equivalent per the Third Law. As a top-level article, it should mention that the term entropy has been used in other fields, with a quick 'taster' of how: I think the current paragraph on "Information entropy" is very good in this respect. A reworking of this article would require reworking of the articles on Thermodynamic entropy, Statistical entropy etc. so that information is not lost (although there is precious little hard information about these concepts in this article at the moment). That's my two euro-cents worth, at least! Physchim62 (talk) 10:52, 19 July 2006 (UTC)

Disorder
Hi,

Although I think the disorder concept is a terrible way to explain entropy (not withstanding the fact that most of the time its just plain wrong), I think that this page needs to retain a reference to the historic use of the words "disorder" and "mixedupedness" - because otherwise some maleducated individual will once again put disorder into this page. Not only that, it will perpetuate the confusion people have as to why disorder is ever used.

So we should have a little paragraph that explains why entropy was explained as "disorder", and why its wrong. Just a short little thing. Fresheneesz 18:11, 21 July 2006 (UTC)


 * Disorder is not wrong. It actually gives a useful intuitive understanding in many cases, and I think most physicists feel comfortable with it (as an intuitive picture). Yevgeny Kats 20:39, 21 July 2006 (UTC)


 * As with many words, the 'wrongness' of 'disorder' depends on the context in which it is used -- and that means more than just the context of a word in a sentence or a paragraph. Context includes the human situational factors -- teaching situation -- human or text, encylopedia situation, group of beginners talking, skilled chemists around a table, or any group of skilled scientists talking with one another...Skilled scientists can use any lingo they wish to communicate with one another, of course !! The historical problem is that the pros and profs who aren't have used the 'inside word' in teaching beginners. Is WP for insiders, or is it for those who have little knowledge of a field?


 * My lengthy -- and correct analysis, that can be abbreviated -- is at 23.1 in Archive2 of this Talk:Entropy. 'Disorder' has been a century-long disaster in texts and teaching situations. Is there any other cause but the exclusive use of 'entropy is 'disorder' for almost universal hate and fear and lack of understanding of entropy by chem students and its misinterpretation even by philosophers and economists? Entropy is not a complex idea at the beginners' level (as my track record of adoption by most gen chem text authors has shown), but because 'entropy is 'disorder' has the vagueness of mystery, kids have thought there's something profound hidden there that they have to understand but never can -- because they are never led to think of what the molecules are doing.


 * Someone else can summarize the history in 23.1 of Archive2, emphasizing that Boltzmann's error was innocent because it was before knowledge of molecular behavior, especially that of quantization of their energies. The meaninglessness of 'disorder' is most clearly shown by the fact that there is no 'order' in any macro (molar) quantity of a substance measurably above 0 K (The Pitzer ref I gave.) Then, of course!, join it to that great paragraph above that was not approved by Nonsuch at Item 15 in this Talk:Entropy section, " "Overview" in WP Entropy Article. Revision of the present 2nd paragraph" FrankLambert 00:24, 22 July 2006 (UTC)


 * Fine fine, "disorder" is not "wrong" - its crappy terminology. However, my point is that I think we need a little paragraph explaining this scientific weirdness. Fresheneesz 01:25, 24 July 2006 (UTC)


 * I would tend to agree with Fresheneesz on the desirability of an explanation of why entropy is not disorder: on the other hand, someone has to write it in an appropriate NPOV manner, which is hardly a simple task. Physchim62 (talk) 14:59, 24 July 2006 (UTC)


 * I do not believe this is an issue with NPOV, as everyone is describing the same physical phenomenon. The difference lies is how you attempt to educate readers in regards to Entropy, outside of pure mathematical models.  Energy distribution is much easier to understand than a vague idea of disorder, especially since disorder is a generalized term that does not fit well with the subject at hand. Physical Chemist 16:42, 28 July 2006 (UTC)


 * Entropy &ne; disorder because disorder is a subjective concept. 2LOT deals only with thermodynamic (as its name implies) phenomena best described as a "spreading out" of energy in all processes, not as an "increase" in some level of disorder (implying that somehow things were "ordered" to begin with).  Note too, that while we can say that there is no entopy at 0K, (absolute zero), this state is unattainable according to quantum physics -- in other words the order we "see" is a function of our perspective.   &#0149;Jim 62 sch&#0149;  19:19, 30 July 2006 (UTC)


 * Have the people here ever looked at a simulations of a gas at one temperature and that of a gas at a higher temperature. They both look like molecules flying through space, one is just faster.  How is that matter "more disordered"?  How is the energy "more disordered"?  It IS more spread out among the translational, vibrational and rotational modes, but is that really more disordered?  I don't even see how that works on a subjective concept?  Hence, I'm in the entropy is not disorder camp. In fact, it's hard for me to write a entropy is not disorder section, because I have trouble seeing it that way.  I might in a  few weeks, though Olin 22:15, 2 August 2006 (UTC)


 * The final nail in the coffin of 'disorder', showing that no chemical system above about 1 K is 'ordered' (and, in fact, all at that temperature and above are astonishingly disordered) is in a peer-reviewed article that is available at http://www.entropysite.com/order_to_disorder.pdf.

Move
Given this edit by Sadi Carnot (which is a valid edit, btw) I propose we move this article (i.e., renasme) to "Entropy (thermodynamics)" and remove anything unrelated to thermodynamics as the other uses are not in keeping with the thermodynamic meaning of entropy, and as they have their own articles. &#0149;Jim 62 sch&#0149; 16:27, 6 August 2006 (UTC)


 * Since the term "entropy" is used mostly in the context of thermodynamics (and statistical mechanics), I'd suggest that the name of the article stays simply "Entropy", rather than "Entropy (thermodynamics)". I don't think anything should be removed from the article. All the other uses of this term are mentioned only briefly, which is good, since they are not unrelated to the thermodynamical entropy. Yevgeny Kats 19:12, 6 August 2006 (UTC)

Except that that misses the point, and ultimately misleads the reader do to a functional, widespread misunderstand of what "entropy" means. And really, the other uses are not truly related to thermodynamics. In those uses, entropy is taken to mean disorder, chaos, in thermodynamics it really means "re-order", it makes no subjective judgment re chaos or disorder. &#0149;Jim 62 sch&#0149; 23:39, 6 August 2006 (UTC)


 * Since there is an entropy disambiguation page, I wouldn't recommend it. I've always found that moving pages in Wikipedia creates more tension than it's worth. Olin 14:04, 7 August 2006 (UTC)

Now I'm confused...if there's an entropy disambig page, why does this article mention non-thermodynamic entropy? &#0149;Jim 62 sch&#0149; 23:10, 7 August 2006 (UTC)


 * Because it's not like one word which incidentally has two different meanings, but these concepts are related. Yevgeny Kats 23:51, 7 August 2006 (UTC)

Loosely, maybe. &#0149;Jim 62 sch&#0149; 00:05, 8 August 2006 (UTC)

Lede
Suggested changes to generalise the concept in clearer terms. "State function" doesnt cut it for an intro, even if "relative measurement" isnt quite correct. Criticism welcome. -Ste|vertigo 18:12, 27 August 2006 (UTC)

Entropy is a concept of a relative measurement of the degree, rate, and vector of energy dispersal within an isolated system, as well as between connected systems. The interpreted meaning depends on the context, for example in physical cosmology "entropy" is a generalised function of all thermodynamic processes in the universe, and is characterised by the notion that universal expansion is a relatively "disordered" process, wheras a singularity represents a "ordered" state in truly isolated systems (such as the universe is theorised to be) the entire energy system is entropic, whereas in connected systems (as found in nature) entropy relates directly to heat transfer.

In thermodynamics, entropy (symbolized by S) is a fundamental part of the second law of thermodynamics, which defines the relationship between time and the energy within an unequilibriated system &mdash; hence it is an important factor in determining a system's free energy to do work. It is measured as a state function of a thermodynamic system, defined by the differential quantity $$dS = dQ/T$$, where dQ is the amount of heat absorbed in a reversible process in which the system goes from the one state to another, and T is the absolute temperature.
 * }


 * May I just say that to a layman the first sentence looks good, and much clearer than what's there just now. Unfortunately the bit after "for example" gets baffling. Presumably the intention is that "universal expansion" is seen as having dispersed or spread out energy, and hence higher entropy, and the opposite with the "singularity". Why the peaceful first option should be seen as "disordered" is obscure. Assuming the singularity is not about obsessive trekkies, a singularity which challenges many conventions in physics and in which general relativity breaks down does not sound a terribly "ordered" state. Though presumably it has rather large energy concentrations. ...dave souza, talk 21:35, 27 August 2006 (UTC)


 * Thanks for your comments Dave. Its typically difficult to make important distinctions for a general topic in a concise way, let alone in a way which will satisfy various specific disciplines in common terms. So, Im using the term "disorder" solely for the purpose of clarifying that improper and misleading generality, as its been propagated by certain people for their own "layman" descriptions. I agree its an obscure view, and AFAIUI, the cosmologist's concept of "order" is something like "Planck nothingness," and anything that actually exists is, by definition, "disordered." So, if that definition qualifies as a dogmatic (mis)generalization of what in technical terms is a rather sophisticated concept, my only guess the dogma is based on the problem that "the Big Bang" has some explosive connotations, and therefore can't exactly be explained as a "smooth" or "peaceful" process. Any changes you want to make to the above, feel free. Id rather work on it here first of course. -Ste|vertigo 22:11, 27 August 2006 (UTC)


 * I really wish everyone would stop with this disordered nonsense. Entropy is not disorder, it is merely a reordering of molecules -- even if molecules are flying around in what appears to our aethetic need for symmetry a "chaotic" manner they are still ordered.  If entropy were true chaos or disorder we'd not be able to explain why the molecules interact as they do as there would be no discernable laws regarding their interaction.   &#0149;Jim 62 sch&#0149;  22:41, 27 August 2006 (UTC)
 * So then its something which can be avoided and therefore left without explanation? Again theres this difference between the quantum world of "energy," and the larger thermodynamic world of "heat." So Im not sure if its good to be specific to the latter, explaining things only in terms of understood molecular processes, and altogether avoid any theorised "quantum" processes which reference the concept "entropy" in a related but different scope. Is it not valid to try to touch on such differences upfront? -Ste|vertigo 06:15, 28 August 2006 (UTC)
 * I have no idea what you're trying to say. Are you sying quantum mechanics allows for, or represents, "disorder"? &#0149;Jim 62 sch&#0149;  09:34, 28 August 2006 (UTC)
 * Quantum mechanics: "Broadly speaking, quantum mechanics incorporates four classes of phenomena that classical physics cannot account for: (i) the quantization (discretization) of certain physical quantities, (ii) wave-particle duality, (iii) the uncertainty principle, and (iv) quantum entanglement. Each of these phenomena will be described in greater detail in subsequent sections."
 * Not to put it bluntly, but if a discipline diverges from classical mechanics in a way that requires its measure of quantities to be both discrete and variable, the properties of its particles to be inherently co-dependent as well as somewhat paradoxically dualistic, and for uncertainty to rule over them all, then I suppose yes that by "disorder" I mean something that is relatively less "ordered" than the better understood classical mechanics. Quantum thermodynamics needs work, so Im not clear about the transitions. -Ste|vertigo 00:32, 29 August 2006 (UTC)


 * In my opinion, the new suggested definition is unacceptable because it's vague and non-standard. Rate?? Vector?? These words have nothing to do with entropy. Yevgeny Kats 06:35, 29 August 2006 (UTC)


 * True Yevgeny.
 * Stevertigo et al: the problem with using the term "disorder" is that the word order as it is commonly used is itself no more than a human aethetic construct and therefore subjective. Humans have come to love and require symmetry, predictability and a sense of "everything in its proper place".  However, these aesthetic needs are diven by our view of the macrocosmos (the world clearly visible to us) as an enviroment wherein the changes that do happen are predictable (hence those that were seemingly unpredictable were ascribed to the gods). Unfortunately, the microcosmos, which is what quantum mechanics adresses, seems less ordered as it is  seemingly  less predictable.  Nonetheless, it is "ordered" in that quanta, particles, etc., do follow certain rules, and if there are any issues in fully understanding the workings of QM it rests solely with us, not in a lack of "order" in the quantum world.
 * Think about it, if these things that appear disordered were truly disordered, they would be by extension chaotic and is all were chaos, especially at the quantum level -- which is the underpinning of the observable world at the macro level -- we'd not be here to discuss order. &#0149;Jim 62 sch&#0149; 09:53, 29 August 2006 (UTC)


 * Indeed, Entropy is a scalar and to use any descriptor with regard to the direction of energy movement would be unphysical. Energy tends to move from a hotter to a cooler system (the 2nd law of thermodynamics), and the Entropy is a measure of this change with respect to the temperature and not time.  Therefore the comment about rate is also unphysical.  Entropy can not be expressed in units of seconds or Hz (inverse time, i.e. rate), and can not be qualified by a direction.  Any change to the article using such terms should be reverted.  That would be confusing to people who are new to Entropy. Cheers, Astrobayes 18:48, 29 August 2006 (UTC)


 * Jim and Astro, thank you for your very direct criticism of the particular concepts of rate and vector in the above version. I will correct those in the draft below --please strike anything improper. Astrobayes: your description is quite clear, although, for someone coming here due to an interest in entropy as it is used (or misused) in cosmology or in QM, one might wonder how any notion of movement can exist without accounting for time. In otherwords there is some aspect of the containment paradox here wherin the definition of entropy itself rests on this notion of a (truly) "isolated system," which would itself to be an unphysical concept. Jim' your statement "it is ordered in that quanta, particles, etc., do follow certain rules" makes it clear that "order" and "disorder" are characterisations rather than descriptions. Though it may be fair to assume that all of physics is (by nature ) "ordered", I had thought my usage of "relatively less" might have sufficiently qualified it with respect to understanding of the local versus the greater. Again, the containment paradox. -Ste|vertigo 21:26, 29 August 2006 (UTC)



Entropy is a concept of a relative measurement of the degree of energy dispersal within an isolated system, as well as between connected systems. The interpreted meaning depends on the context, for example in truly isolated systems (such as the universe is theorised to be) the entire energy system is entropic, whereas in connected systems (as found in nature) entropy relates directly to heat transfer.

It is measured as a state function of a thermodynamic system, defined by the differential quantity $$dS = dQ/T$$, where dQ is the amount of heat absorbed in a reversible process in which the system goes from the one state to another, and T is the absolute temperature.
 * }


 * Stevertigo, you ask a good question: "...one might wonder how any notion of movement can exist without an accounting of time." And the answer lies in the fact that Entropy, an extensive scalar variable of a system, is a very special mathematical object called an  exact differential.  Its value as a physical descriptor, and its mathematical value, only depends upon the initial and final states of any system and that system's environment.  A great analogy to this scalar case is the path-independence of a conservative force which is a non-rotational vector field, expressable as the gradient of a scalar.  This information should help to resolve any issues regarding concepts of time, rate, or direction in the Entropy article.  I'm going to give this article another read-through, b/c it's been too long since my last read and I've neglected the poor thing.  Perhaps I can make some useful contributions. Cheers, Astrobayes 21:47, 29 August 2006 (UTC)


 * Great. Thanks. Yes its confusing, so perhaps it needs to state the context first in a way which defines what Entropy is and what it is not, &mdash;the measurement of two relative states of temparature within a finite system, ultimately is a concept that would appear to have nothing directly to do with any continuous phenomenon in nature --as one may be led to believe. -Ste|vertigo 20:31, 30 August 2006 (UTC)

GA Re-Review and In-line citations
Note: This article has a small number of in-line citations for an article of its size and currently would not pass criteria 2b. Members of the WikiProject Good articles are in the process of doing a re-review of current Good Article listings to ensure compliance with the standards of the Good Article Criteria. (Discussion of the changes and re-review can be found here). A significant change to the GA criteria is the mandatory use of some sort of in-line citation (In accordance to WP:CITE) to be used in order for an article to pass the verification and reference criteria. It is recommended that the article's editors take a look at the inclusion of in-line citations as well as how the article stacks up against the rest of the Good Article criteria. GA reviewers will give you at least a week's time from the date of this notice to work on the in-line citations before doing a full re-review and deciding if the article still merits being considered a Good Article or would need to be de-listed. If you have any questions, please don't hesitate to contact us on the Good Article project talk page or you may contact me personally. On behalf of the Good Articles Project, I want to thank you for all the time and effort that you have put into working on this article and improving the overall quality of the Wikipedia project. Agne 00:19, 26 September 2006 (UTC)

Utterly ridiculous nitpick
Two important consequences are that heat cannot of itself pass from a colder to a hotter body
 * First of all, this is a statistical effect, so the theory really states that it is statistically improbable for this to occur. Second of all, heat does flow from colder to warmer bodies spontaneously (through all of the usual mechanisms), it just so happens that more flows in the other direction.  It is like a chemical reaction that is reversible but biased.  Yes, this is a ridiculous nitpick, but seriously is it impossible to get more accurate wording here?  It's not like there's a magic one-way valve that prevents a colder object from radiating towards a warmer object - indeed the amount of this radiation is terribly important in many calculations involving heat shielding, etc.  -- JustinWick 01:03, 27 September 2006 (UTC)


 * I feel your pain on this one and not too long ago I tried, vehemently, to get momentum going for an article improvement to address problems such as you raise here. The result was that my edits and comments (and those of other users such as Frank Lambert) were hotly contested by a select few individuals and were usually changed.  I have left this article alone until the embers cooled a bit.  Perhaps we can look into an SPR in the near future?  Many physics articles have been discussed on SPR recently and have gained a lot of positive ground.  And doing so would involve a community of individuals with an interest in the physical accuracy of this article, rather than a point of view.  Cheers, Astrobayes 03:16, 27 September 2006 (UTC)


 * I don't think its a ridiculous nitpick. However, I doubt that South Park Republicans (SPR) have anything to do with entropy. PAR 04:44, 27 September 2006 (UTC)
 * Firstly, sounds like an important correction to me: presumably it should read "are that it is statistically improbable fo heat of itself". Secondly, when I looked back at this page for info it had once again lapsed into the incomprehensibility that does so much to add to the mystique of entropy, but does nothing to explain it to beginners. I've therefore added a citation from Frank Lambert to the intro, which in my opinion helps to make the article understandable. ...dave souza, talk 08:40, 27 September 2006 (UTC)

Evolution
The intro included evolution as another field of study in which the concept is used, but the only reference I've found in the article is to HG Wells' fictional "devolution", and in the evolution article it appears as a common misconception, so I've removed it pending explanation. ...dave souza, talk 08:26, 28 September 2006 (UTC)


 * It's used by creationists (quite wrongly) to "disprove" evolution, however, it has no relevance in that context.  &#0149;Jim 62 sch&#0149;