Talk:Introduction to entropy/Archive 2

Moving Forward With Improving This Article
After weeks of trying to be truly collaborative, my patience has expired. I apologize for once again coming off as rude, but moving forward, I will be working with editors, , , and anyone else who can demonstrate a responsible and reader-empathetic understanding of the mission here: to provide an introductory explanation of entropy for laypersons. The discussion is verging on disruptive behavior, and again I think such energy would be better spent on improving the other entropy articles, rather than this introductory overview, which requires a special hand.

This article needs to be short, it needs to be in plain language, and there should be little or no math. It should provide a light survey of the various applications of entropy, with links to their respective articles. Some exacting technical rigor may need to be sacrificed to accomplish this mission. I am sorry, but it gets clearer by the day that the mission will not be accomplished otherwise. I daresay the consensus, among the new contributors combined with the long history of comments above, cries out for the article to be much more accessible and less technical and exacting.

I will proceed by preparing an animation, and I look forward to reading DrPippy's contributions. Also, a fair warning: Inappropriate or unwelcome responses in this section may be moved to an earlier section. I am over the walls of text and mathematical minutiae. The English major or the financial analyst we edit for doesn't care about degrees of freedom, or phase spaces, or $$\int_0 ^{S_f} \mathrm d W(S,V)$$. None of that is helpful here. We are going to move forward with improving this article and getting it to where it needs to be.  -Jord gette  [talk]  23:30, 1 December 2020 (UTC)


 * Okay, I've taken an initial crack at drafting an intro which (hopefully) strikes the right balance between encyclopedic tone and accessibility. I've tried to incorporate (1) a basic definition of entropy as an expression of the number of arrangements corresponding a particular state (without talking about multiplicity, microstates, or macrostates!); (2) an illustration of the second law; and (3) examples of irreversibility and disorder.  I can think of many problems with my current draft (not the least of which is the lack of citations), but hopefully it's a decent starting point.  So here's what I have at the moment:


 * In thermodynamics, entropy is a numerical quantity which describes the number of different ways that the constituent parts of a system can be arranged to get the same overall arrangement. For example, there are many ways to arrange the molecules of a gas inside its container that yield the same temperature and pressure; any two molecules could be swapped, but the overall state of the system would remain unchanged.  If the gas were moved to a larger container, the number of possible arrangements of the constituent molecules would increase greatly; the entropy would therefore be larger as well.


 * The second law of thermodynamics is one of the foundational principles of physics; it states that entropy tends to increase over time. A gas which is initially confined to only the lower half of its container will quickly expand to fill the upper half of its container as well.  From the standpoint of entropy, this is a result of the fact that there are many more ways to arrange the gas molecules in the entire container than there are to arrange them in only half of the container.  Thus the entropy of the gas increases as it expands to fill the container.  (Note: I think a figure here could be useful.  Maybe a 2-molecule "gas", which would only have one way to have both molecules in the bottom half, but two ways to have one molecule in each half, implying that it's twice as likely for this "gas" to fill the container than to remain confined at the bottom.  I can make a figure like this, but it won't happen until the weekend!)


 * The second law implies that some processes cannot be undone. The process of scrambling an egg increases its entropy, as there are many more ways to arrange the egg molecules in a scrambled state than there are to arrange those same molecules with an intact yolk separated from the white.  The scrambling process essentially randomizes the positions of the egg molecules; once the egg is scrambled, it is practically impossible for continued stirring to cause all of the egg molecules to happen upon one of the relatively few arrangements where the yolk and white are separated, and so an egg cannot be unscrambled. (Note: I can imagine other analogies here that might be considered more encyclopedic; perhaps mixing two liquids, or lighting a match?  I think this version works fine, but I'm not opposed if someone would prefer a different illustration.)


 * Entropy is often considered to be a measurement of disorder. This equivalence, while not always applicable, is generally practical because disordered states almost always have higher entropy than ordered states.  There are relatively few ways to organize a deck of cards so that it is separated by suit compared to the number of arrangements where the suits are mixed together. There are relatively fewer ways to organize the objects in a room in a tidy fashion compared to the number of haphazard arrangements.  There are fewer ways to arrange pieces of glass into an intact window than a shattered window.  A shuffled deck, a messy room, and a broken window all possess more entropy than their more well-ordered counterparts.  The second law therefore implies that it is relatively easy for a highly-ordered system to become disorganized, but much more difficult to bring order to a disorganized system.


 * I'd love to hear any feedback; feel free to edit this as mercilessly as necessary! DrPippy (talk) 00:28, 2 December 2020 (UTC)


 * Great start; thank you. Do you think the article should be moved back (renamed) to Introduction to entropy? Because I think it would be great to have a general "introduction to entropy" article that touches on all of its aspects and interpretations, and can serve as a portal to the various non-introductory entropy articles. Perhaps "Introduction to thermodynamic entropy" is too specific for an introductory article. If I were that English major or financial analyst, I might stumble on the first two words being "in thermodynamics" (they might well not know what thermodynamics is).


 * As I've mentioned a bunch of times on this page, I feel strongly that the first paragraph should mention the popular meaning of the word, as the current version does: The word 'entropy' has entered popular usage to refer a lack of order or predictability, or of a gradual decline into disorder. Many people come to this article having seen the word in that context, and the article needs to help them. If we were to move this article back to Introduction to entropy, perhaps the first paragraph can mention that entropy has various subtly different applications in various disciplines, and that the word has also entered popular usage. Then the 2nd paragraph can launch into the thermodynamic account, and we're off to the races.  -Jord gette  [talk]  17:10, 2 December 2020 (UTC)


 * I originally thought yes, the article should be renamed Introduction to entropy; now I'm not too sure. The problem is in physics and thermodynamics entropy seems to be part of natural science: it has a clear definition as the number of microstates corresponding to a state, and natural consequences; it controls the direction of spontaneous processes seen in nature.  The wider applications of entropy appear more artificial.   It will be hard to explain to general readers the connection of the thermodynamic definition to the entropy of a text message, or an image, or a computer program, or a chess position.  I think it should be renamed, but most of the article should still concentrate on the thermodynamic application. --ChetvornoTALK 19:22, 2 December 2020 (UTC)
 * I agree with Jordgette above the common meaning of entropy as "disorder" could be earlier in the intro. --ChetvornoTALK 19:36, 2 December 2020 (UTC)


 * It does make sense to move the disorder stuff earlier. I'd be uncomfortable with this in the lead; since it follows from the multiplicity definition rather than the other way around, I think you need to have the multiplicity definition under your belt to understand why entropy can be understood in terms of disorder.  Would it be okay to keep the first paragraph more or less as is, but then immediately segue into the disorder paragraph?  I think I can move things around pretty easily.


 * If I make changes to the original draft, is it okay to overwrite the original draft (just so the talk page doesn't get too long)? Or would it be better to post the whole thing from scratch?  Either way, I can take another crack at this later tonight or tomorrow.


 * Lastly, I agree with renaming the article Introduction to entropy. The word "thermodynamic" is an unnecessary barrier to entry for the non-technical reader, and when the concept of entropy comes up in the context of a popular audience, I feel like it's almost always talking about the thermodynamic sense.  Might not be a bad idea to include a (short) section on entropy in other contexts where you could look at Shannon entropy, etc., but I would actually be okay excising that material from this article. DrPippy (talk) 21:42, 2 December 2020 (UTC)
 * I guess my point is that if we change the name we can't excise it completely, the article will have to at least mention all the types of entropy. But maybe the more abstract types should be included WP:SUMMARYSTYLE, in brief paragraphs with links.  I think we should resist the tendency of statistical thermodynamicists to include a lot of mathematics, which will simply not be understood by 99% of readers coming to this introductory article. --ChetvornoTALK 22:23, 2 December 2020 (UTC)


 * Much preferable to post the whole thing from scratch. Changes made to a talk page post can easily make nonsense of another editor's  response to the initial version. It is talk-page convention to allow for that. If there has been no response, changes are usually reasonable.Chjoaygame (talk) 22:04, 2 December 2020 (UTC)


 * Agree that it could be better to go back to the  title Introduction to entropy, and with the related suggestions. Reservation: as to the general structure of the article, I continue to agree with Editor PAR, that the logic of the article should be primarily grounded in thermodynamic entropy. There are valuable generalisations or extensions of the notion of entropy in statistical mechanics, mathematics,  and informatics, and I see it as probably a good idea to indicate them in the article.Chjoaygame (talk) 22:41, 2 December 2020 (UTC)

New draft of introductory paragraphs
Here's my latest draft:
 * In popular usage, entropy is often considered to be a measurement of disorder. This usage stems from the physical definition of entropy as a numerical quantity which describes the number of different ways that the constituent parts of a system can be arranged to get the same overall arrangement.  For example, there are many ways to arrange the molecules of a gas inside its container that yield the same temperature and pressure; any two molecules could be swapped, but the overall state of the system would remain unchanged.  If the gas were moved to a larger container, the number of possible arrangements of the constituent molecules would increase greatly; the entropy would therefore be larger as well.


 * The equivalence between entropy and disorder arises because disordered states almost always have higher entropy than ordered states. There are relatively few ways to organize a deck of cards so that it is separated by suit compared to the number of arrangements where the suits are mixed together. There are relatively fewer ways to organize the objects in a room in a tidy fashion compared to the number of haphazard arrangements.  There are fewer ways to arrange pieces of glass into an intact window than a shattered window.  A shuffled deck, a messy room, and a broken window all possess more entropy than their more well-ordered counterparts.


 * The second law of thermodynamics is one of the foundational principles of physics; it states that entropy tends to increase over time. A gas which is initially confined to only the lower half of its container will quickly expand to fill the upper half of its container as well.  From the standpoint of entropy, this is a result of the fact that there are many more ways to arrange the gas molecules in the entire container than there are to arrange them in only half of the container.  Thus the entropy of the gas increases as it expands to fill the container.  (Note: I think a figure here could be useful.  Maybe a 2-molecule "gas", which would only have one way to have both molecules in the bottom half, but two ways to have one molecule in each half, implying that it's twice as likely for this "gas" to fill the container than to remain confined at the bottom.  I can make a figure like this, but it won't happen until the weekend!)


 * The second law, taken in combination with the relationship between entropy and disorder, implies that it is relatively easy for a highly-ordered system to become disorganized, but much more difficult to bring order to a disorganized system. Furthermore, some processes cannot be undone at all.  The process of scrambling an egg increases its entropy, as there are many more ways to arrange the egg molecules in a scrambled state than there are to arrange those same molecules with an intact yolk separated from the white.  The scrambling process essentially randomizes the positions of the egg molecules; once the egg is scrambled, it is practically impossible for continued stirring to cause all of the egg molecules to happen upon one of the relatively few arrangements where the yolk and white are separated, and so an egg cannot be unscrambled.

This addresses the popular view of entropy = disorder right off the bat, but also keeps the physical definition in the first paragraph. Not sure about the overall flow, but I think we're moving in the right direction! DrPippy (talk) 22:36, 2 December 2020 (UTC)


 * Very unhappy to see the traditional but confusing 'disorder' interpretation being proposed to overwhelmingly dominate the article. The tradition is a major reason why entropy puzzles people.


 * It would be a retrograde step to help it continue to overwhelmingly dominate, when the 'spread' interpretation is so much easier and more intelligible, and is now also mainstream. There is good literature objection and criticism of the confusing tradition. The article would probably be unnecessary if the regrettable 'disorder' interpretation hadn't taken on. Editor DrPippy didn't answer my question about how he had found the 'spread' interpretation in the empiric of teaching.


 * It is unhappy, even misleading, or even mischievous, to say that entropy "tends" to increase over time. It increases in every non-trivial thermodynamic process. Better not to fudge that in the vague word "tends". Thermodynamic entropy refers to discrete states of thermodynamic equilibrium. It is not a continuously time varying quantity, and it is poor pedagogy to allow a hint to the contrary. Boltzmann's $$H$$ function can be regarded as an 'entropy' only in a derivative or highly technical sense. Thermodynamic entropy gets its character from the unique symmetry of thermodynamic equilibrium, which is a strictly unchanging state. Phil Attard in Sydney is proposing a proper extension of the concept of entropy to non-equilibrium conditions, but that is a project for the future, far outside the scope of this article.


 * The process of scrambling an egg is an unhappy instance to use as a prime example of the second law, because scrambling is not a simple example of a natural or spontaneous process; it implies a personal stirrer. Talk of stirring and manual arranging of molecules distracts from the key to the second law, that the molecules naturally rearrange themselves. A boiled egg is a simpler but more subtle example, because it does not call upon a person to scramble the white and the yolk; it is not very suitable for our purpose. I dislike the words "essentially randomizes". They are vague and allude to a bundle of distracting and dubiously relevant concepts.Chjoaygame (talk) 23:37, 2 December 2020 (UTC)

first revision of DrPippy's draft
In thermodynamics, entropy is a measure of the possible diversity of arrangements of the constituent parts of a body of matter and radiation. For example, there are many ways in which the molecules of a body of gas can arrange themselves inside its container with one and the same temperature and pressure; any two molecules can be swapped while the overall state remains unchanged. If the gas is allowed to spread into a larger container, the number of accessible arrangements of the molecules increases greatly; the entropy increases to indicate that.

The second law of thermodynamics is well established. Beyond the just-mentioned example, another is in two different gases that are initially separated into two compartments by a partition in a container. When the partition is removed, the gases spread themselves throughout the container. The total entropy increases in this process because there are many more ways in which the different gas molecules can arrange themselves in the entire container than in the separated compartments. (Note: this is the place for the animation mentioned above, as proposed by Editor Chetvorna. Such an animation would truly earn this article a place in Wikipedia. Anyone?)

More generally, the second law says that natural spontaneous processes do not undo themselves. When a match is lit, it spreads light, heat, and matter. It cannot unlight itself. To reconstitute a fresh match requires an elaborate manufacturing process, which could hardly recapture the scattered matter of the original match.Chjoaygame (talk) 01:50, 2 December 2020 (UTC)


 * This version seems inferior to me. The crucial fact that entropy is a numerical measure is not mentioned.  The word "diversity" seems out of place.   "The Second law of thermodynamics is well established." is totally without context, it isn't mentioned again until the next para., and the central point that the 2nd law says entropy can never decrease in a spontaneous process is omitted.  The description of the match example makes it sound like a reduction of entropy can only occur in a manufacturing process.  --ChetvornoTALK 19:59, 2 December 2020 (UTC)


 * Thank you for your comment. Action taken. The 'never decreases' version refers to the trivial case of a "process" that doesn't actually proceed, or to the imaginary or fictive theoretical limiting case of a reversible "process". Those special, unnatural, or highly technical cases unnecessarily distract from the main fact expressed in the second law, that in a spontaneous process, entropy always increases. I like the word 'diversity' there.Chjoaygame (talk) 22:18, 2 December 2020 (UTC)

update
In thermodynamics, the entropy of a body of matter and radiation is a physical quantity that measures the spread or accessible range of distribution of motions of its microscopic elementary components. For example, there are many different ways for the molecules of a body of gas to move around inside its container, with one and the same temperature and pressure. If the gas is allowed to expand into a larger container, the range of accessible different motions of the molecules increases; that is measured as a numerical increase in entropy.

Such an increase of entropy illustrates an important physical principle, the Second law of thermodynamics. Another simple example of increase of entropy according to the law is when, into a body of gas in a container, heat is allowed to spread from its surroundings, giving its molecules a greater accessible range of speeds of motion and rotation. Another process described by the law is in two different gases that are initially separated into two compartments by a partition in a container. When the partition is removed, so that a greater volume becomes accessible for each of them, the molecules of the gases spread themselves to move throughout it. In this process, the total entropy increases because more ways have become accessible for the different gas molecules to move around in the entire container than were accessible in the separated compartments. (Note: this is the place for the animation mentioned above, as proposed by Editor Chetvorna. Such an animation would truly earn this article a place in Wikipedia. Anyone?)

More generally, the second law says that natural spontaneous processes of interaction between bodies do not undo themselves, and that this is always evident in an increase of entropy. In contrast, for a decrease of the entropy of a body, an organised expenditure of energy is necessary. For example, when a match is lit, it consumes oxygen and spreads light, heat, and matter with a corresponding increase of entropy. It cannot unlight itself. To reconstitute a fresh match requires an organised process, which could hardly recapture the scattered matter of the original match.

The word 'entropy' has entered popular usage to refer a lack of order or predictability, or of a gradual decline into disorder.Chjoaygame (talk) 12:58, 3 December 2020 (UTC)

welcoming
Great to see we are making some solid progress. I think the first paragraph should be welcoming and give the reader a chance to settle in before launching into the physics. This is what I'd propose:

"Entropy is an important concept in physics, specifically the field of thermodynamics, and in information theory. The word has also entered popular usage as a measurement of the disorder of a system, or to refer a lack of order or predictability, or of a gradual decline into disorder.[citation] A more physical interpretation of entropy refers to the spread of energy or matter in a system. Entropy shows that many physical processes can go in only one direction in time — for example, even in a perfectly sealed room, a puff of smoke will dissipate into the air, but it will never reform into a concentrated puff. To understand how the physical interpretation led to its interpretation in information theory (as well as its popular interpretation), it helps to consider the thermodynamic origins of the term and how they tie into the field of physics known as statistical mechanics."

I'd also like to make the unspeakable proposal that the lead section of this article contain only one paragraph. It seems difficult, if not impossible, to provide a gloss of entropy's various interpretations that is appropriate for a lead section; it gets weedy very quickly, and that's intimidating for a lay reader who has not even reached the body of the article. I further propose that after such a bare-bones lead paragraph, the body of the article begins with the first section, Entropy in thermodynamics...something similar to thermodynamics-focused paragraph below.

The animation is coming along. It's essentially 200 boxes, with 100 red balls and 100 blue balls, and I'm using a random number table to determine the motion of each ball from frame to frame. It would have been easier to write a program, but unfortunately I have to do it manually because I don't have those skills. But I'm doing it in Blender, so it should look pretty good.  -Jord gette  [talk]  17:29, 3 December 2020 (UTC)


 * A few suggestions:


 * In popular usage, the word 'entropy' means lack of order or predictability, or gradual decline into disorder. The word originated in physics, in the field of thermodynamics, where it refers to the natural spontaneous spread of matter and radiation, or of energy, into all the the diverse forms of motion and places to which they have access. For example, in a sealed room, a puff of smoke will irreversibly disperse, and will not concentrate itself again. Though it occurs according to the laws of physics for microscopic particles, in order to make calculations about such dispersal, it has helped to regard it as random or probabilistic, in a branch of physics known as statistical mechanics. In turn, this has been studied in engineering terms, in information theory. This led to highly mathematical analysis of the evolutions of various motions.


 * For accuracy as an illustration of the second law of thermodynamics, an animation will show first the equilibrium of motions in two separate compartments, followed by the removal of the partition, leading to the spreads of the different coloured balls into a new equilibrium of motion.Chjoaygame (talk) 19:26, 3 December 2020 (UTC)


 * I don't care for the explanation of entropy in terms of "spread" of energy or matter; this is one consequence of the second law, but I'm doubtful that it's the most important one. I don't believe that using this concept as the basis for the explanation of entropy is a standard approach (even in a popular definition), nor well-supported by the physics.  I'd have a hard time getting behind any definition that doesn't start from the idea of looking at the number of microscopic arrangements that lead to the same large-scale state, as this is really the basis for all the other ways of thinking about (physical) entropy, whether you prefer disorder, dispersal/diffusion, irreversibility, or anything else. DrPippy (talk) 18:39, 3 December 2020 (UTC)


 * I am sorry to see Editor DrPippy feeling so. Entropy is about motion, and to talk just about 'arrangements' misses much of the nature of entropy. As for support in thermodynamics and chemistry, it would be hard to find more authoritative sources than Edward A. Guggenheim and Peter Atkins. Nowadays, there are many textbooks that use the 'spread' language because their authors find it helps for teaching beginners, which is closely relevant for this article. Again, it would be hard to find more authoritative sources of reasoned physical objection to the more traditional 'disorder' view than Edwin Thompson Jaynes and Walter T. Grandy, Jr, on the grounds that it is obscure and baffling.Chjoaygame (talk) 19:52, 3 December 2020 (UTC)


 * I don't have strong opinions about number of paragraphs in the lede, or how those paragraphs are organized, but I do feel very strongly that the first paragraph needs to have some appropriately-wordsmithed version of "a numerical quantity which describes the number of different ways that the constituent parts of a system can be arranged to get the same overall configuration." Otherwise, you're really talking about the effects of the second law, rather than what entropy is. It's great to be non-technical, and if that means we sacrifice some degree of precision in terms of the nitty-gritty details then that's a sacrifice well worth making.  But I don't think this means we should fail to provide a non-mathematical but physically accurate definition of entropy in the first paragraph, and none of the alternatives that I've seen so far do this. DrPippy (talk) 18:39, 3 December 2020 (UTC)


 * A physically accurate picture of physical entropy requires more than an account of configurational arrangement: it requires also an account of motion. That is why phase space is used, rather than merely configuration space. Guggenheim's 'spread' and 'dispersal' are good ordinary language words to express entropic motion.Chjoaygame (talk) 23:10, 3 December 2020 (UTC)


 * I hear you. I am doing what I can to prevent readers from being scared off by the first paragraph, which is the monumental challenge here. What do you think of this version:


 * "Entropy is an important concept in physics, specifically the field of thermodynamics, and in information theory. The word has also entered popular usage as a measurement of the disorder of a system, or to refer a lack of order or predictability, or of a gradual decline into disorder.[citation] As a numerical measure, entropy describes the number of ways that components of a system (such as the molecules of a gas) can be arranged in order to result in the same overall configuration. If such a system is allowed to change without any external influences, the number of those arrangements — i.e., the system's entropy — invariably goes up with time, never down. This fact is captured in an important law of physics known as the second law of thermodynamics. A consequence of the second law of thermodynamics is that many physical processes can go in only one direction in time. For example, even in a perfectly sealed room, a puff of smoke will dissipate into the air, but it will never reform into a concentrated puff. The closed system of air-plus-smoke begins with low entropy, and it ends with high entropy: the smoke is evenly distributed throughout the room, and at that point (known as thermodynamic equilibrium), any random movement of air or smoke molecules will still result in the smoke being equally distributed. At equilibrium, the system's entropy has reached its maximum value."


 *  -Jord gette  [talk]  19:29, 3 December 2020 (UTC)


 * Spontaneous and diverse motion is crucial to physical entropy. To say that 'components can be arranged' obscures this. The components move spontaneously, without waiting passively for an agency to arrange them. It is true that counting numbers of ways of arrangement is helpful as a mathematical approximation, but it misses motion as a key aspect of entropy.Chjoaygame (talk) 20:04, 3 December 2020 (UTC)


 * The use of arrangements as distinct from motions is a mathematical device, and is short on physical content. One of our principles here is to avoid mathematics. Our interest is in physics.Chjoaygame (talk) 22:12, 3 December 2020 (UTC)


 * The importance of diversity of motion has been carefully brought to our attention by Editor PAR, when he has emphasised that entropic spread is in phase space. The words 'diversity of motion' render motion in phase space in ordinary non-technical language.Chjoaygame (talk) 21:23, 3 December 2020 (UTC)


 * The words "evenly distributed" miss the diversity of entropic motion. Guggenheim's word 'spread' better expresses that diversity.


 * To be more explicit than "many physical processes", one could say something such as 'minglings amongst the components of bodies of matter and radiation'. In contrast, such processes as planetary orbiting are not very helpful illustrations of the second law.Chjoaygame (talk) 22:32, 3 December 2020 (UTC)


 * The clause "Entropy is an important concept in physics, ..." is hardly necessary. People who read or write in this article will mostly already have decided that entropy is an important topic. Indeed, we mostly think that everything in Wikipedia is important. The space taken up by that clause could probably be better used.Chjoaygame (talk) 06:37, 4 December 2020 (UTC)


 * I object strongly to a phrase like "As a numerical measure, entropy describes the number of ways that components of a system (such as the molecules of a gas) can be arranged in order to result in the same overall configuration." This is NOT the definition of THERMODYNAMIC entropy. This is a description of INFORMATION entropy as applied to EXPLAIN thermodynamic entropy. To blur the difference between the two is a disservice to the reader, no matter how new they are to the subject. It does not simplify things, it outright confuses the issue. The idea that thermodynamic entropy and information entropy are distinct is not rocket science. The change in thermodynamic entropy is a measured macroscopic experimental quantity that has nothing to do with atoms, molecules, microstates, macrostates, probabilities or any of those statistical mechanical concepts. The laws of thermodynamics are experimentally observed relationships between these macroscopic measurements, again with no reference to statistical mechanics. Information entropy is a mathematical construct which Boltzmann used, along with a number of ASSUMPTIONS, unverified experimentally, to very successfully EXPLAIN thermodynamic entropy and the laws of thermodynamics. Information entropy is NOT thermodynamic entropy and to purposely obfuscate the difference in the name of simplicity is wrong. The distinction is simple, to blur it does not produce simplicity, it produces an outright falsehood. The new user who does not pursue the subject walks away with a false idea of thermodynamic entropy, and those who do pursue it will eventually discard this article as so much hogwash. PAR (talk) 03:40, 5 December 2020 (UTC)


 * Broadly speaking, I agree with this comment by Editor PAR. We may observe that it was written with the article title 'Introduction to thermodynamic entropy' in mind. Because of the complexity of the problem, 'information entropy' is more a program for research than a complete physical account.Chjoaygame (talk) 11:53, 5 December 2020 (UTC)


 * Likewise a phrase like "The word originated in physics, in the field of thermodynamics, where it refers to the natural spontaneous spread of matter and radiation, or of energy, into all the the diverse forms of motion and places to which they have access." This is a blatantly false statement. Thermodynamic entropy refers to a measurement involving thermodynamic parameters, and it's magic is that it is a state variable. The change in entropy between A and B is independent of the path taken to get there. Now the struggle begins to intuitively understand it. "disorder", "spreading", these are all initially useful but ultimately incorrect ways of characterizing entropy, "disorder" being the worst offender, because it refers to the information entropy interpretation. "Spreading" at least deals with effects very often (but not always) associated with a change in thermodynamic entropy. The essential experience of thermodynamic entropy is irreversibility. This is what the second law says and that is ALL it says, and that is a simple concept to illustrate. Thermodynamics does not presume to explain it, only to define it and characterize it via the second law, and statistical mechanics does not presume to define it or characterize it, only to explain it and to explain the second law. PAR (talk) 03:56, 5 December 2020 (UTC)


 * I am replying to Editor PAR's above comment referring not to the draft by Editor Jordgette that leads this section 'welcoming', but to my offering above under the line ″A few suggestions″. I feel I need to defend myself from the charge made by Editor PAR in his comment. He writes ″Likewise a phrase like "The word originated in physics, in the field of thermodynamics, where it refers to the natural spontaneous spread of matter and radiation, or of energy, into all the the diverse forms of motion and places to which they have access." This is a blatantly false statement.″ Editor PAR writes as if I had written something such as 'thermodynamic entropy is spread'. No, I wrote that the word refers to spread; of course, PAR is right in objecting that 'spread' is not the thermodynamic definition of entropy. I have written many times above that 'spread' is an interpretation, intending to make it clear that an interpretation is not a definition. I think that what I wrote is perfectly consistent with Editor PAR's sentence ″Thermodynamic entropy refers to a measurement involving thermodynamic parameters, and it's magic is that it is a state variable.″ For me, there is a big difference between saying what a word refers to and saying what is its definition, or what it is. I am deliberate in using the word 'refers'.


 * In more detail, I am sorry to see Editor PAR giving less credit to the 'spread' interpretation than I think it deserves. Editor PAR has repeatedly, and in my view rightly and importantly, said that if the word 'spread' is to be used in this context, then it should properly include 'spread' of instantaneous states in microscopic phase space, and should not be limited to spread in ordinary physical space. Intended to say just that in ordinary language are my above words ″into all diverse forms of motion and places to which they have access″. In particular, my words ″all diverse forms of motion″. If those words of mine fail to convey, in ordinary language, what Editor PAR is referring to, then I have failed to adequately articulate my thoughts. I intend by those words to avoid the technicality of phase space, which I think it is not convenient to name explicitly or define in the very most introductory part of the article. My understanding of Editor PAR's right insistence on considering the full depth or intricacy of the phase space description is, to the best of my power, indicated by the words ″diverse forms of motion.″ Perhaps some more helpful rendering of this important idea into ordinary language may come forth for us.Chjoaygame (talk) 11:37, 5 December 2020 (UTC)


 * I don't like the sentence ″At equilibrium, the system's entropy has reached its maximum value.″ It can too easily be read to suggest that entropy grows gently towards thermodynamic equilibrium. This belies the discrete character of thermodynamic processes, and underplays the fine precision, or in Editor PAR's word, 'magic', in the quantity 'entropy'. Moreover, and more concerningly, it slips towards a vague notion of 'maximum'. Maximum with respect to what range of possibilities?Chjoaygame (talk) 12:28, 5 December 2020 (UTC)


 * I think it worth noticing that Editor Jordgette is using a random number table to determine the motion. My point is that he is using a mathematical table as a convenient way of modeling the system, instead of using a calculation that fully implements the laws of motion. In other words, he is virtually using a probability approach as a mathematical trick, not as a really physical account. I am not objecting to his doing so, just pointing out the difference between probability theory and physics that was noted by Guggenheim.Chjoaygame (talk) 12:15, 5 December 2020 (UTC)

I'm going to be honest; I think I really prefer the approach in my (second) version. (Definite need for wordsmithing, and probably could be a little clearer in places.) I think that most or all of the issues that Chjoaygame has raised are red herrings in terms of the purpose of this article (although certainly interesting from the standpoint of philosophy of science.

I think the article (at least the intro) really needs to do only one thing: it needs to connect the popular conception of entropy (disorder/chaos/decay, although maybe this is shaped by me playing too many videogames) with the scientific one. The physical reason that the second law leads to greater disorder is that there are (vastly) more disordered states than ordered states; similar arguments apply to irreversibility, diffusion in physical or phase space, etc. The only requirement is that there needs to be some mechanism causing the system to randomize its (micro)state; the laws of probability and the Central Limit Theorem take care of the rest. Whether that mechanism is a person with a spoon stirring cream into a cup of coffee, the thermal motion of constituent molecules, or the machinations of the Flying Spaghetti Monster and His Noodly Appendage is not important to the very narrow purpose of explaining, in layman's terms, what entropy is, and how that idea helps us to understand the world around us.

As to the spread interpretation, two points: (1) it's a consequence of the nature of entropy and the second law, not a description or explanation of it; (2) this interpretation of entropy hasn't captured popular attention the way the disorder interpretation has. We need to work with what the popular interpretation is, not what we want it to be. (FWIW, I don't think either disorder or spread is a good model for the fundamental nature of entropy; as I've said before, entropy is fundamentally defined in terms of probability.)

I think we need to be very careful to avoid unnecessary complexity; there's a time and place to take a look under the hood and think about what's really going on, but almost never when you're introducing a new idea. DrPippy (talk) 13:08, 5 December 2020 (UTC)


 * I just saw PAR's objection a few paragraphs above; unfortunately it's a bit hard to keep track of everything that's happening on this talk page!


 * Not to be overly blunt, but I am in complete disagreement with his point. The statistical physics definition of entropy (Boltzmann/Gibbs; the two are essentially equivalent in an isolated system) is (1) a physical definition of entropy, predating and unrelated to informational entropy; (2) can be shown to be equivalent to the thermodynamic interpretation dS=dQ/T (see the math-box in Entropy_(statistical_thermodynamics)); and (3) offers a relatively clear explanation for related phenomena in a way that the macro-scale thermodynamic equivalent does not.  For the purposes of this article, this third point is the most important one.


 * Is it possible this is a physics/chemistry disagreement? My experience is that physicists will start with a definition of entropy based on microscopic arrangements (k ln W), whereas the chemists find more use in the macro-scale thermodynamic interpretation (dQ/T).  In either case, I would generally argue that in general the macroscopic laws used in physical chemistry are a result of the statistical mechanics of large collections of microscopic particles, and therefore the interpretation of entropy given by statistical physics is more fundamental. The sentence that PAR is objecting to is my best attempt to put this interpretation into non-technical language.  I'm very open to improved wording, but I'd argue strenuously against using a different interpretation. DrPippy (talk) 13:08, 5 December 2020 (UTC)

Proposed move to Introduction to entropy
Re. PAR's comment in previous section:  We talked above about moving the article to Introduction to entropy, thus including information entropy. This seemed to be favored by a majority of you (and me). Maybe this should be decided before going on, since it will have an impact on the introduction. Shall we move the article?--ChetvornoTALK 05:38, 5 December 2020 (UTC)
 * Agree as above --Bduke (talk) 06:20, 5 December 2020 (UTC)
 * Agree --ChetvornoTALK 07:37, 5 December 2020 (UTC)
 * Indifferent --Chjoaygame (talk) 10:14, 5 December 2020 (UTC)
 * Agree DrPippy (talk) 12:16, 5 December 2020 (UTC)
 * Agree -- -Jord gette  [talk]  15:22, 5 December 2020 (UTC)


 * ✅ Consensus, performed move --ChetvornoTALK 21:05, 6 December 2020 (UTC)


 * The archive of the talk page is yet to be  moved.Chjoaygame (talk) 00:24, 7 December 2020 (UTC)


 * I have moved the archive of the talk page, I hope correctly, following the technique as I read it from PAR. Perhaps someone experienced in such moves may check what I have done.Chjoaygame (talk) 06:24, 8 December 2020 (UTC)

Problems with the "Heat and entropy" section
This section appears to be focused on justifying the interpretation of the entropy change in a phase change as a spatial "spreading" of energy. It then concludes with the statement that "The important overall principle is that energy of all types changes from being localized to becoming dispersed or spread out, if not hindered from doing so." and that "Entropy (or better, entropy change) is the quantitative measure of that kind of a spontaneous process: how much energy has been transferred/T or how widely it has become spread out at a specific temperature."

This is simply wrong. The entropy of mixing at equal pressure and temperature involves no spatial spreading of energy or energy/T. The energy density is constant. Furthermore, it is fair to say that energy "spreads out" among all degrees of freedom, and to say that energy only spreads spatially is to say that energy can only spread out in the spatial degrees of freedom, which contradicts the first statement. This belongs in the "Introductory descriptions of entropy" section. PAR (talk) 19:03, 11 December 2020 (UTC)


 * I removed the "Heat and Entropy" section and, since it appeared to be written by a proponent of the "energy dispersal" idea, I expanded the "Energy dispersal" section with references, and including the energy dispersal quote. PAR (talk) 03:02, 14 December 2020 (UTC)

footnote style calls for editorial re-think
There are two footnotes in the lead that are formatted as references.

Their logics are not far enough from 《I have just said 'X', but more precisely I should have said 'not X'.》 Deeply poor style, not Wikistyle (my neologism I guess). They call for thorough editorial re-thinks. Supposing there is still a place for footnotes, they should be formatted as footnotes, not as references, though, in  my view, footnotes are by their nature usually poor style for Wikipedia, and are much better avoided altogether.Chjoaygame (talk) 22:51, 15 December 2020 (UTC)

Two Questions
I have been sitting out because I was very happy that we got something into the first paragraph that answers the question for lay readers looking to learn what entropy, in the context of popular usage, means. That said, I have two questions for the presently active editors here:

1. Why is there a section about information entropy in an introduction to thermodynamic entropy? Should the article be moved back to Introduction to entropy?

2. Are you planning to eventually revise the article so that it is a non-technical introduction, either to thermodynamic entropy or entropy in general? Or maybe all of this work should be directed at the main entropy articles instead? Because except for certain sentences, this article is nowhere close to being a non-technical introduction to anything. Frankly, it is a disaster in that respect. Consider: "counterexamples may be included in the concept of 'dispersal' when the 'space' in which the dispersal occurs includes the space of quantum energy levels versus population numbers". If you think this is appropriate for a non-technical introduction article, then either you're working on the wrong article(s), or you're the wrong people to be working on this article. Non-technical means non-technical. Perhaps you have been so deep in physics for so long that a sentence like this appears non-technical and appropriate for a general audience. It isn't. I don't mean this as an insult, but rather as a wake-up call. I fear that the objective here has been lost a long time ago, and this needs to be pointed out.

Perhaps when the present editors are done deciding what goes into the article and where, I can go through it and draft a non-technical version, appropriate to a general audience, for your consideration.  -Jord gette  [talk]  23:51, 24 November 2020 (UTC)


 * In answer to question 1, its because the full picture of thermodynamic entropy cannot be seen without the understanding provided by information entropy. Would you rather simply have the description of how to measure thermodynamic entropy, say that it increases, and then walk away?


 * In answer to question 2, I agree, that sentence is too technical, and needs to be restated. This article is a hodgepodge of 10 or 20 editors, and I think at least we have a passable introduction. Please, if you can, simplify things where it is needed. PAR (talk) 02:14, 25 November 2020 (UTC)


 * In answer to question 1. 'Information entropy' is a form of words with a perhaps regrettable history. The word 'entropy' in 'information entropy' was arbitrarily stolen from physical conceptions of entropy. That theft was perhaps unfortunate, but to go beyond the everyday idea of 'spread', the ideas that underlie 'information entropy' are necessary. They include the idea that matter and radiation are composed of many microscopic material particles such as molecules, and of many photons. If you are happy to leave things just with the everyday idea of 'spread', then this article could forget about such things as molecules and photons, and forget about 'information entropy'. That would be a simplification.


 * Going further, perhaps, as you suggest, particularly bearing in mind our readers who are not interested in physics, the article could even forget about thermodynamic entropy. In that case, the article could scale down into your sentence "The word 'entropy' has entered popular usage to refer a lack of order or predictability, or of a gradual decline into disorder."  Indeed, the article would then be practically an item for a dictionary of ordinary language.


 * Alternatively, the view that the article should be strongly non-technical could be abandoned. Instead, the article could attempt to explain the physics of entropy for readers who would like to learn a bit more than highscool physics.Chjoaygame (talk) 06:15, 25 November 2020 (UTC)


 * Remember that Wikipedia has many different articles on entropy covering different aspects. I continue to believe that an article with Introduction in the title should be a non-technical introduction, and only mention the advanced aspects briefly with links to appropriate articles for those who are interested. And an article with Thermodynamic in the title should be primarily about heat, work and energy at a macroscopic level. Disorder can be explained qualitatively with links to the more mathematical aspects, and information theory can be mentioned briefly with a link for more detail.


 * As for the statement that the term entropy in information theory was "stolen" from thermodynamics, I would prefer to say "copied". If I steal your property, you don't have it any more. If I copy your book or other intellectual property, you still have access to it and can use it. Thermodynamics still uses the term "entropy" even if it is also used elsewhere. Dirac66 (talk) 16:13, 25 November 2020 (UTC)


 * Editor Dirac66 is sober and tactful, as well as being wise. I think it relevant here that von Neumann gave, as reason for his suggestion, that no one knows what entropy is, and that it would consequently help Shannon in debates. I used the word 'stolen' in order to emphasise that unsavoury aspect of the history. With respect, I will defend it by noting that Editor Jordgette proposes to emphasise, by giving it a sentence in the most widely read spot of the article, the first paragraph of the lead, the regrettably traditional and misleading "disorder" interpretation, and that Editor Dirac66 still suggests it. Gresham's law at work. In such a pickle, distraction is near to theft of meaning. Breach of copyright is in some respects like theft. I defer, however, to Editor Dirac66's remark that the word can still be used in thermodynamics.


 * It is still open to Editors to change the title of the article. It is still open to Editors to restrict the main lines of the article to macroscopic thermodynamics, with a bare minimum of reference to the particulate aspect of thermodynamic bodies.


 * Editor Dirac66 proposes a distinction between non-technical and advanced aspects of the article. Perhaps he is suggesting that a microscopic account is 'advanced' and 'technical'? If, as he seems to suggest, a 'non-technical' account is primarily macroscopic, the new presence of 'thermodynamic' in the title would suggest that the case against a microscopic account would be strong. Displacing Clausius' prior 'disgregation' interpretation, the 'disorder' interpretation was invented on the basis of the microscopic account, and makes what little sense it has on that basis. On the other hand, the 'spread' interpretation makes sense for the macroscopic account; 'disgregation' is nearly synonymous with 'dispersal'.Chjoaygame (talk) 20:15, 25 November 2020 (UTC)


 * Thank you. We have something in the first paragraph to help out readers who are not interested in physics — that's great. The rest of the article should be for people who are interested in physics, but not (yet) versed in the jargon and mathematics — for example, a high schooler taking high-school physics, a financial analyst doing cross-disciplinary research, or a biologist studying the fundamental properties of living systems. Note that the main Entropy article links to this one as, "For a more accessible and less technical introduction to this topic...." So it should at least be more accessible and less technical. The disambiguation page links as "an explanation on entropy as a measure of irreversibility." Perhaps this article is biting off too much in trying to cover everything?


 * I'll be happy to help out with accessibility once the content and roadmap have reached, um, a kind of equilibrium.  -Jord gette  [talk]  16:57, 25 November 2020 (UTC)


 * This is the opinion of an electronic engineer. It's obvious that all of you have put a great deal of effort into improving this introduction, and it's pretty ingenious.  Congrats!  I can see I'm entering a very mature discussion.  So this is just my impression, looking at the introduction as a nontechnical reader would:


 * I agree that the introduction should be made simpler for general readers. There will be middle school students, high school dropouts, English majors and overworked single mothers trying to get through community college coming to this article.  The discussion of irreversibility and coffee is good.  But I'm not sure it's possible to explain thermodynamic entropy to general readers without going into what it means at the particle level.  That means introducing some statistical thermodynamics concepts as is done in paragraph 4, in particular the concept that entropy measures the number of "microstates" available to the system.  And anyway that is the link to the common meaning of the word as "disorder".   Maybe it makes sense to forget the distinction between thermodynamic and statistical entropy and move this article to Introduction to entropy.  But I think the statistics needs to be dialed back in the intro; it should be limited to concepts and not include any mathematics.  In particular, I don't think the digression into coin flipping in the last two paragraphs belongs in the introduction.  --ChetvornoTALK 19:18, 25 November 2020 (UTC)


 * Thank you, Editor Chetvorno, for your comment. I agree that the 'disorder' interpretation relies on the particle account, while I add that the 'dispersal' interpretation works for both the bulk and the particle accounts.Chjoaygame (talk) 20:26, 25 November 2020 (UTC)


 * I agree with the concept of a non-technical introduction that will be meaningful to the layperson, and I appreciate all the hard work and thought that has gone into this article over the years. With that said, if the goal is to explain what entropy is, I think the probabilistic definition needs to be front and center (based on the definition $$S= k \ln W$$).  At its most fundamental level, entropy is simply a description of how probable a particular state is.  Entropy appears related to the concept of disorder simply because disordered states are more probable than ordered states: there are a lot more ways to arrange a pile of carbon, hydrogen, and oxygen atoms as a scrambled egg than there are to arrange those atoms as an intact, unscrambled egg.  Irreversible processes are irreversible because when you switch (micro)states more or less at random, you're far more likely to end up in the more probable state: you expect to beat a scrambled egg and have the yolk and white spontaneously separate for the same reason you wouldn't expect to shake a shoebox with a hundred coins (or more realistically, a few trillion trillion coins) (it's a very big shoebox in this analogy) and have them all come up heads.


 * The common definitions in terms of disorder, unavailable energy, reversibility, etc. all stem from the fundamental nature of entropy as a measurement of probability, and I think the article would be both clearer and more accurate if that were our starting point. DrPippy (talk) 18:42, 28 November 2020 (UTC)


 * Thank you, Editor DrPippy, for your thoughts. In order to define the probability of a state, one first needs a definition of a state. A 'thermodynamic state' is a persistent object, one that is compatible with many distinct 'microscopic states'. Then one needs a definition of a microstate. It may be an instantaneous or a persistent object. It may itself consist of a single 'state' or of a class of single 'states'. And one needs a definition of a probability, an object that refers to a suitable sample 'space'. The sample 'space' then needs definition. Without such definitions, the interpretation of entropy in terms of probability is vague, or incomprehensible. To write out such definitions is to go beyond the ordinary bounds of the 'non-technical'.


 * I think it is loose to say that "disordered states are more probable than ordered states". In Boltzmann's formula, the states are equally probable. It is difficult to define a distinction between disordered and ordered states. I think that notions of "disorder, unavailable energy, reversibility" are interpretations, not definitions, of entropy.


 * In summary, I think that the matter is not too simple.Chjoaygame (talk) 20:15, 28 November 2020 (UTC)


 * You're right, of course, that a detailed explanation of microstates vs macrostates is likely to be too technical to be useful to the intended audience here. I think as a practical matter, when people talk about the "state" of a system in ordinary English, they mean the macrostate: e.g., temperature rather than position and velocity of each constituent molecule, etc.  When I've talked about the second law/entropy/etc. in classes for non-science majors, I've generally found that even the relatively science-phobic students have a relatively intuitive sense of what I mean when I say "probability of a particular state", or talk about high-entropy states being more likely than low-entropy states.  The traditional coin-tossing example—flip two coins, there's two ways to have a head and a tail, but only one way to have two heads or two tails, etc.—has generally seemed pretty accessible, and might be a useful illustration in this article.  I've generally found it unnecessary to dive into a more detailed explanation of the technical concepts involved in order to introduce the basic idea of entropy, and it seems like we're in agreement that getting too far into the weeds here would be counterproductive.


 * I don't think that defining entropy in terms of probability is inherently more confusing than the other definitions. (In fact, it generally seems to clear up a lot of confusion about what entropy is.)  More to the point, the other definitions of entropy are at best misleading, if not outright incorrect. DrPippy (talk) 21:58, 28 November 2020 (UTC)


 * Thank you for your further thoughts. You observe that “even the relatively science-phobic students have a relatively intuitive sense of what I mean when I say "probability of a particular state".” Without wishing to be personal, I guess that you are a persuasive teacher. You write “I don't think that defining entropy in terms of probability is inherently more confusing than the other definitions.” Further, you write “More to the point, the other definitions of entropy are at best misleading, if not outright incorrect.” Which other definitions? Are you intending to mean that Guggenheim is outright incorrect in his proposal of the 'spreading', 'dispersal', and 'accessibility' interpretation? And that Peter Atkins has let himself be led up the garden path by it? (By the way, I have no hesitation in thinking that Atkins allows himself grandiose delusions about the scope of the second law.) You haven't told us how the 'spreading' interpretation goes down in your classes. For me, the idea that heat spreads, and that diffusion is a kind of spreading, and that the expansion of a gas into a newly accessible space is a form of spreading, are intuitively attractive accounts. They make no appeal to probability, and marginal appeal to the molecular nature of matter. I think they have a fair claim to being 'non-technical'.


 * I think it important to distinguish macroscopic and microscopic viewpoints, and to distinguish definitions from interpretations. Boltzmann's so-called 'probability' interpretation refers not necessarily to probability, but necessarily to a number of 'states'. That is why Planck uses the qualified term 'thermodynamic probability', to refer to something nearer to the reciprocal of probability. Boltzmann's 'states' are said to be 'equiprobable'. From the microscopic viewpoint, I think it useful to distinguish 'probability' from 'extent of specification'. The latter names in other words what is customarily called 'quantity of information', defined by Shannon's function, in the topic of coding theory or combinatorics, also known as informatics. Some writers propose that 'probability' in this context is better interpreted in terms of informatics.


 * Blind application of the 'probability' interpretation has a problem in dealing with Poincaré's recurrence theorem.


 * There are two elements in the 'probability' account. 'That a process increases the probability of something.' It needs some explanation as to why a probability would change. The increase is due to new accessibility for spread. And 'that a macrostate's possible microstates are equiprobable.' Uniform spread comes to mind.Chjoaygame (talk) 02:29, 29 November 2020 (UTC)


 * I think you are over complicating things. This article is an introduction. It is the material I used to teach to chemistry students in the second year of an Australian or UK 3 year chemistry degree. You are just over complicating everything! --Bduke (talk) 09:06, 29 November 2020 (UTC)
 * I agree. We are going to have readers much less educated than college students coming here: middle school students, HS dropouts.  A Wikipedia article also doesn't have as much space as a chemistry textbook chapter to get this stuff across.  I guarantee you that English majors are going to have a hard time understanding what coin flipping has to do with stirring cream into coffee.  We need to get much more simple and concrete.  Diagrams would help a lot.  Kittel p.47, fig. 2.9  has a series of simple diagrams of boxes of point particles showing things that increase entropy: adding particles, adding thermal energy, increasing the volume, decomposing molecules. --Chetvorno<i style="color: Purple;">TALK</i> 09:41, 29 November 2020 (UTC)


 * [Deleted unnecessary rambling] I ran across this article: https://www.space.com/43138-life-is-chaotic-entropy.html. I think it does a nice job explaining a physicist's view of entropy to a popular audience (including some of the intricacies of microstates vs. macrostates, etc.) without getting too bogged down in technical detail. Could we use something like this as a starting point? I'm happy to draft some text here if it'd be helpful to have something concrete to critique. DrPippy (talk) 15:22, 29 November 2020 (UTC)


 * I agree with the above three editors. It would benefit Wikipedia to have an article that shows how coin-flips and coffee-stirring have the concept of entropy in common, for readers who don't need to see the derivations of equations. But the desire for textbook rigor continues to make even the lead of this article unnecessarily opaque. Which is why I suggested that such intensive work go toward improving the non-introductory entropy articles instead.


 * A previous version of the lead used this example of billiard balls, and for the purposes of connecting probability to mixing, I would like to see it re-inserted:


 * "Consider a billiards table with 15 balls on it. If we broadly observe that the balls are all lined up along one edge of the table, there is a certain finite number of combinations of the individual balls' locations that would be consistent with that broad observation of the balls being lined up in such a manner. However, if we broadly observe that the balls are spread out across the table (perhaps in a seemingly random arrangement), then there is a much higher number of combinations of the individual balls' locations that would be consistent with the broad observation that the balls are spread out. We say that the spread-out arrangement has high entropy, compared to the lined-up arrangement's low entropy."  -Jord gette  [talk]  18:27, 30 November 2020 (UTC)


 * A nearly disqualifying aspect of the coffee-and-cream example, at least for me, is that usually I stir the cream into my coffee with a coffee spoon. The point of the second law is that the spread occurs spontaneously, without intervention by an animate agency, such as me and my spoon. Yes, if I waited all day without stirring, a deal of spreading would occur spontaneously, but my coffee would be cold by then, and so I would perhaps have thrown it out.Chjoaygame (talk) 19:48, 1 December 2020 (UTC)
 * You have a point. It will probably not be clear to newbies that the diffusion and increase of entropy will occur without stirring.  The experiment does show the unidirectional nature of entropy, as no amount of stirring will return the coffee to the microstate it was originally in, with the coffee and cream separated.  But it could be misleading.  There are other examples without stirring, like if you leave a perfume bottle open the room will soon smell of perfume, or if you put an ice cube in a glass of still water it will come to a common temperature. --Chetvorno<i style="color: Purple;">TALK</i> 20:30, 1 December 2020 (UTC)

for ease of editing
For weeks, this discussion has gone in two (or more) very different directions. How are we going to resolve this?  -Jord gette  [talk]  18:27, 30 November 2020 (UTC)
 * Yeah, it sounds like the debate is bogged down in vague generalities. I think the only solution is to start proposing specific wording, as Jordgette did, either here or editing the article per WP:BRD.  Then editors can say what they think about specific sentences and paragraphs, and consensus wording can be thrashed out.    My personal feeling is that the introduction should be aimed at middle school students in the spirit of WP:ONEDOWN.   So there should be no math, and the debate about proper terminology should be saved for the article body; if the word "disorder" in the intro helps teenagers understand, use it.   I kind of like the general explanatory approach taken on the website  proposed by DrPippy, (if the unencyclopedic hip entertaining teen style and room cleaning similes are edited out).   if you want to write a version, go ahead.  --Chetvorno<i style="color: Purple;">TALK</i> 21:43, 30 November 2020 (UTC)


 * Aw, but I like the hip entertaining room cleaning similes! (In all seriousness, I do think these sorts of analogies are by far the best way to communicate technical concepts to a non-technical audience, even if they're not completely encyclopedic.) I'm hashing some stuff out on my sandbox right now and I'll post something here when I've got something that might not be terrible. Would welcome any feedback and suggestions both before and after. DrPippy (talk) 21:49, 30 November 2020 (UTC)
 * Well I hear you but we do have standards (WP:EPSTYLE). Actually I'm not sure that any of these similes - billiard balls, coin flips, disorganized bedrooms - are going to help the low-level readers they are aimed at.  A lot of nontechnical readers do not have any understanding of things on an atomic level - they are not aware that a cup of coffee sitting still is actually composed of particles moving randomly at high speed.  Maybe it would be better to just explain what's going on without similes.  I think diagrams would help more.  A series of diagrams showing a box with red balls on one side and blue balls on the other diffusing into one another when the partition is lifted, would explain increase of entropy on an atomic scale.  It would explain the coffee & cream example directly.  Or better yet, an ANIMATION showing such diffusion! --Chetvorno<i style="color: Purple;">TALK</i> 23:06, 30 November 2020 (UTC)


 * Editor Chetvorno makes a good suggestion. His word "diffusion" is pretty close in meaning to the more general terms found in the literature, the 'disgregation' of Rudolf Clausius, and the 'spread', 'dispersal', and 'accessibility' of Edward A. Guggenheim. Guggenheim in 1949 wrote


 * Various attempts have been made to describe entropy in simple language. An unpublished fragment by W. GIBBS 5 suggests that entropy is a measure of the extent to which a system is mixed up.


 * Lord KELVIN is supposed to have suggested that entropy measures the extent to which a system is run down. Another suggestion will be made below, but before this is done it must be emphasized that whatever it may be that entropy measures for an isolated system, this same something is measured for a system in a thermostat by Massieu's function.


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




 * In conclusion it may be pointed out that nowhere has the word 'probability' been used. The popular statement that a system has a natural tendency to change from less probable to more probable states is in the author's opinion stretching the word 'probable' beyond its recognized meaning.


 * It took some years till the 'spread' interpretation found its way widely. I don't know of an earlier or more authoritative expression of it than Guggenheim's. I would be glad of enlightenment on this point.Chjoaygame (talk) 00:51, 1 December 2020 (UTC)


 * I would love to take on the animation. There's a strong argument that such a visual representation will get the concept across more immediately and clearly than examples and similes made of words.  -Jord gette  [talk]  17:14, 1 December 2020 (UTC)


 * For the sake of unambiguity, with, I trust, the permission of Editor Chetvorno, I here quote precisely his above admirable words:


 * Maybe it would be better to just explain what's going on without similes. I think diagrams would help more. A series of diagrams showing a box with red balls on one side and blue balls on the other diffusing into one another when the partition is lifted, would explain increase of entropy on an atomic scale. ...  Or better yet, an ANIMATION showing such diffusion!


 * This is a simple, direct, and accurate account of the molecular view of the second law.Chjoaygame (talk) 17:34, 1 December 2020 (UTC)


 * It explicitly indicates the initial condition of systems separated by a partition, which is then a lifted so  as to produce a final state. For all we know, the animation after the lifting might run long enough to occasionally exhibit Poincaré recurrence!Chjoaygame (talk) 22:54, 1 December 2020 (UTC)


 * Thanks, that's what I meant to say.--Chetvorno<i style="color: Purple;">TALK</i> 21:25, 1 December 2020 (UTC)
 * Didn't mean to sound so negative above. I could live with the billiard ball example.  You (as well as the other editors here) have experience.  You clearly have ideas. I'd say go ahead and write the introduction you'd like to see, to get things started. --Chetvorno<i style="color: Purple;">TALK</i> 21:25, 1 December 2020 (UTC)
 * If you can make a diffusion animation, that would be awesome!  I've done some animations, just freehand GIFs drawn in SVG, but the ideal way to do this would be in MATLAB.  I have just a tiny bit of experience with MATLAB, I'm nowhere near able to do that. --Chetvorno<i style="color: Purple;">TALK</i> 21:25, 1 December 2020 (UTC)

@Dr. Pippy - regarding the "messy room" versus the "orderly room", I think this discussion should go in the "Introductory descriptions of entropy" section, which lists convenient, but ultimately misleading explanations of entropy. The reasons for their helpfulness, and where they break down should be listed here. The order/disorder idea is breaks down when you realize that the vague concept of "order" must be defined before the concept can make any real sense. If I take a desk that looks very messy by the conventional standards and write down the location and orientation of every potato chip and crumpbled piece of paper and say "that is what I define as an orderly desk", then there are many possible clean desks that, by my definition, deviate from my ordered desk and are therefore disordered, and so the entropy of a conventionally ordered desk is larger. It's more a matter of how much information does it take to describe the stuff on the desk, not how "ordered" it is. For my definition of an ordered desk, it takes no extra information, for the "clean" desk, it takes a lot of information to express its deviation from my "ordered" desk, and even more to describe a conventionally messy desk other than my standard.

@Jordgette - The billiard ball example is another example of the order/disorder concept. You say that there are more ways for the balls to be spread out on the table than there are for them to be lined up. But if you take a photo of one case of the spread out balls, there are many ways for the balls to be different from that, including the one where they are lined up. You have defined "lined up" to mean order, but I have defined a particular "spread out" configuration to define order, and neither one of us is wrong. Entropy is a measure of how many ways there are to deviate from whatever you want to call an "ordered" situation. You say that putting them in a line is "ordered", as in y=ax+b. What if its not a first order polynomial, but carefully arranged according to a second, third, or fourth order polynomial? Then your linear order will be very disordered. The order/disorder ultimately requires a definition of order, and ultimately that translates into knowing where everything is, not that it appeals to some vague intuitive idea of order. Again, I think this belongs in the "Introductory descriptions of entropy" section where both the positive and negative aspects of these type of ideas are laid out.

@Chjoaygame - The idea that thermodynamic entropy is the spatial "spreading" of energy and/or mass is simply not sufficient. It assumes that the spatial degrees of freedom are the only ones that can be out of equilibrium. A microstate is represented by a single point in phase space, and the set of microstates (even the nonequilibrium ones) that a system can be in forms a subset of the phase space, or, equivalently, a "volume" in phase space. The logarithm of this volume is proportional to the entropy and is dominated by equilibrium states.

For example, if we have an ideal monatomic gas, fixed volume V and internal energy U, the phase space will have 6N dimensions, 3N spatial degrees of freedom, 3N momentum degrees of freedom. The positional part of the phase volume will be restricted by the fixed volume V and the momentum part will be restricted by the fixed energy with U=p2/2m. The equipartition theorem says that, at equilibrium, all degrees of freedom will contain, on average, an energy of kBT/2. In other words, the energy "spreads out" over all degrees of freedom (assuming they can share), subject to the above constraints. Saying that entropy is spatial spreading is saying that only the spatial degrees of freedom can be out of equilibrium, which then proceed to equilibrium.

In the entropy of mixing example, considering both gases on either side of a container, the phase space will have 12N dimensions, 6N for gas A, 6N for gas B. In the beginning, the phase volume will be separated into two parts, with gas A occupying only part of the phase volume assigned to the position of the A molecules, and gas B only occupying a part of the volume assigned to B. The idea that entropy is a spatial spreading of energy implicitly assumes that the momentum degrees of freedom are unimportant since they are already equilibrated by the fact of the common temperature. The energy will then "spread out" into the unoccupied positional degrees of freedom and entropy will increase. Spatial energy spreading occurs.

This need not be the case. We might just as well assume that the positional DOF's are already equilibrated and the momentum DOF's are not. For example, if we have a plasma, which is a gas at high enough temperature so that there are free electrons and ions, and we subject this plasma to an electric field, the electrons will acquire an "equilibrium" temperature which is higher than that of the ions, due to their much smaller mass. If the electric field is "turned off", the electrons and ions will thermally equilibrate to the same temperature and the entropy will increase. There will have been no spatial spreading of energy or mass. I know, the existence of the electric field implies an external "machine" (battery, capacitor, whatever) and it's not cut and dried, but the point is that in the instant after the electric field is turned off, the system is in a state that is practically the same as just before it was turned off, which shows that such a state is not physically impossible. We don't need the analog of a removable wall to illustrate the point.

As another example, we could postulate a diatomic ideal gas with rotational degrees of freedom. Suppose the spatial and momentum degrees of freedom are all at one equilibrium temperature and the rotational degrees of freedom at another. The rotational degrees of freedom will then equilibrate with the others, arriving at a common temperature and the entropy will increase. There will have been no spatial spreading of energy. I can't think of a real-world example of this situation, but that doesn't mean there isn't one, and besides, we don't need the analog of a removable wall. In the entropy of mixing, we don't need a removable wall, it's just a practical way of establishing the initial condition. We can simply postulate that there are two different gases occupying two sides of a container, both at the same temperature and pressure, and carry on from there.

What I am trying to say is that tying an increase in entropy to a spatial spreading of energy is a special case, based on a number of unnecessary assumptions and therefore does not give a true account of entropy. As a spread of energy in phase space, yes, but assuming that spread only involves the positional degrees of freedom, no. PAR (talk) 22:24, 1 December 2020 (UTC)


 * Agreed. Quite right. The rigorous account is about spread in phase 'space', not merely in ordinary physical space. The article should say so. It remains true that if ordinary spatial spread can occur because of new spatial accessibility, the second law says it will occur spontaneously. The spread in phase space is more conceptually advanced, and will require a suitable exposition in the advanced parts of the article.


 * Some small points. The nominal primary topic of the article is entropy. The definition of entropy is not the same kind of logical object as an account of a thermodynamic process such as is considered in the second law, which is subsidiary in the article. The removable wall is important, even essential, to give an adequate account of a thermodynamic process. The wall, and the thermodynamic operation that lifts it, are discussed in high quality textbooks. The wall is logically necessary, not just a practical way, for the thermodynamical equilibrium of the separated initial condition that occurs in the full statement of the law. A thermodynamic equilibrium has a practically infinite duration, from its past, or into its future, or is bounded by well time-separated thermodynamic operations; it is nothing like an instantaneous state. The zeroth law tells us that if two systems, each in its own respective internal thermodynamic equilibrium, are in thermal connection, they will have the same temperature. For a relevant initial condition exhibiting different temperatures, there needs to be a wall to prevent thermal connection. With respect, that you can't think of a real-world exception is telling; you are a good thinker. In finer detail, every instantaneous state that is eventually visited by the trajectory in phase space belongs to the thermodynamic equilibrium that defines the trajectory. The trajectory traverses a wild diversity of instantaneous states. That is why the Poincaré recurrence time is relevant. It tells how long it takes for a traversal of all those instantaneous states.Chjoaygame (talk) 23:52, 1 December 2020 (UTC)


 * Re the Poincare recurrence time - rethinking it, the Poincare recurrence idea has no place in classical thermodynamics. Classical thermodynamics is about systems in the the thermodynamic limit of infinitely large systems, in which the Poincare recurrence time is infinite - i.e. it never happens. PAR (talk) 11:45, 2 December 2020 (UTC)


 * There is a difference of viewpoint here. The proposition, that "classical thermodynamics is about systems in the thermodynamic limit of infinitely large systems", is, with respect, one that I find, shall I politely say, unacceptable. It comes from a mindset of statistical mechanics as the foundation, which I regard as foreign to classical thermodynamics as such. In my reading, classical thermodynamics is founded in finite macroscopic bodies such as are tested in experiments. Such bodies may be considered from a statistical mechanical viewpoint, as being composed of finitely many molecules. For statistical mechanics, it may be convenient to say that the number of molecules is so large as to be, for mathematical purposes, virtually infinite. I think that if, contrary to the classical thermodynamic view, the system were taken to be founded as an infinitely large body, then the notion of the Poincaré recurrence time would be nonsense. The state of thermodynamic equilibrium in classical thermodynamics has an infinite aspect, in its duration in time, which will far exceed the Poincaré recurrence time. For classical macroscopic thermodynamics, Poincaré recurrence, referring to instantaneous microscopic states, is, of course, foreign. But I think it makes good sense for the statistical mechanical analysis of a finite body.Chjoaygame (talk) 14:15, 2 December 2020 (UTC)


 * Regarding the need for a wall, or its equivalent, to separate various degrees of freedom, you may be right, but I am not convinced. For the mixing example, the system with the wall is described as two different gases in mutual equilibrium, but occupying different parts of the container. Is this description valid an infinitesimal time after the wall is removed? I am saying it is. Are you saying it is not? If it is a valid description of what amounts to a non-equilibrium state, then the fact that a wall produced it is irrelevant. Maybe this argument is insufficient to prove that it is possible for entropy to increase by spreading only into non-spatial degrees of freedom because the wall used to prepare the initial state has not been specified. However, I don't think a convincing argument has been made that, in principle, such a wall can only exist for spatial degrees of freedom, which is what you would need in order to show that entropy increase is unavoidably associated with a spatial spread of energy. PAR (talk) 11:45, 2 December 2020 (UTC)


 * Yes, the gases are still separate an infinitesimal time after the wall is removed. In that infinitesimal time, there are instantaneous microscopically specified states, but a state of thermodynamic equilibrium is not an instantaneous microscopically specified state. It is a long lasting macroscopically specified state. During its life, it can be described by a trajectory in microscopically specified phase space, each point of which is an instantaneous state.


 * I am very uncomfortable with your terms 'non-equilibrium state' and 'equilibrium state' here. We are here not interested in non-equilibrium states as macroscopic entities. For me, the term 'non-equilibrium state', as I read you, would refer to an instantaneous microscopic state that was constructed to belong to a trajectory that described a transient process, that is to say a process that started and ended with distinctly different defining or constitutive macroscopic parameters. Such a trajectory does not belong to a state of thermodynamic equilibrium such as we are studying here. A state of thermodynamic equilibrium has strictly persisting unchanging defining or constitutive macroscopic state variables, extensive or intensive as the case may be, as I have detailed above. Every point in a thermodynamic equilibrium trajectory belongs to its defining thermodynamic equilibrium, and no point in that trajectory specifies a 'non-equilibrium' microscopically specified instantaneous state. There are tracts which baffle themselves, and perhaps others, by mistaking this.


 * If the wall is immovable and impermeable, then 'mutual equilibrium' is the same as separate internal equilibria, and the word 'mutual' is practically redundant, or indeed misleading.


 * I think my position hasn't been made clear. The proper view is that 'spreading' is a description of the exploration of phase 'space' by the above-mentioned trajectory. I think you would find that acceptable? I agree with your point that such is not precisely, rigorously, and fully described by the phrases 'spread of energy in ordinary physical space' or 'spread of matter in ordinary physical space'. But it remains true that when a thermodynamic operation removes a partition, then mostly there will be spread of energy or matter in ordinary physical space. If it is desired to start the article with a full, rigorous, and precise statement, then I agree that such a statement must refer to spread in phase 'space', which I think is your point? But this article, as I understand the desires of our fellows colloquers, is primarily introductory and pedogogical. For this purpose, one may choose to start with a gentle approach, not full and rigorous. A full and rigorous account, referring to phase 'space', could follow deeper into the article, if such were desired. I find that the notions of spread of matter and energy in ordinary physical space seem useful for pedagogical introduction. I regard them as not misleading, and merely as lacking full detail and precision.Chjoaygame (talk) 14:23, 2 December 2020 (UTC)


 * I don't have a problem with the idea that entropy is very often characterized by a spatial spreading of energy or mass, but I would have a problem if it was implied that it is always characterized in this way. The idea that the bottom line essence of entropy is to be found in the spatial spreading of energy or mass should never be proposed, and it doesn't need to be proposed in order to keep things simple.PAR (talk) 17:34, 2 December 2020 (UTC)


 * I agree that "the bottom line essence of entropy is to be found in the spatial spreading of energy or mass should never be proposed, and it doesn't need to be proposed in order to keep things simple". I don't propose so. But I see it as helpful to use the words 'spread' and 'accessible' in an initial introduction, without asserting them as an explicit formal interpretation. In agreement with your view, an explicit formal interpretation should note that the proper bottom line idea refers to phase 'space'. I also agree with  Editor Chetvorno that the interpretative similes such as 'disorder' and 'spread' don't need explicit formal notice as distingished interpretations.Chjoaygame (talk) 23:57, 2 December 2020 (UTC)


 * Ok, I will put some words into the introduction to that effect and see how it flies. PAR (talk) 14:10, 3 December 2020 (UTC)


 * Ok.Chjoaygame (talk) 14:36, 3 December 2020 (UTC)

This is an article introducing entropy. Everything above should have no part in this article. It makes it too complicated. I have taught physical chemistry in several universities. The first year courses really do not say much about entropy. It is mostly introduced in a second year course called "Physical Chemistry". OK, this may not match the situation in the US exactly but it is my experience in UK and Australia. Almost everything above should not be included in such a course. It could be in the entropy article, but not in this introduction. --Bduke (talk) 00:16, 2 December 2020 (UTC)


 * I agree completely. The reason for the discussion, though, is to decide how to simplify things. Do we say, in simple terms, that entropy is the spreading of energy in physical space and put it in the introduction, or do we say that spatial spreading of energy is a helpful but ultimately flawed way of viewing entropy and put it in the "Introductory descriptions of entropy" section? PAR (talk)


 * I concur with the just foregoing remarks of Editor PAR, that the reason for the above discussion is to decide how to simplify things, and that the details of the above discussion are not intended to appear in the article.Chjoaygame (talk) 14:15, 2 December 2020 (UTC)

There seems to be two points of view, the idea that thermodynamics is fundamental and that statistical mechanics as explanation of thermodynamics is subordinate, and 2) Statistical mechanics is fundamental and thermodynamics is a special case of, and derived from, statistical mechanics. I don't think either can be "proven" to be correct. I found a very interesting web page at http://www.av8n.com/physics/thermo/ which takes the second point of view. The author (Denker) has given a lot of thought to the subject of thermodynamics and statistical mechanics and makes some very good points. He sees "entropy" as basically information entropy, and all things flow from that. He give a good criticism of the "dispersal" and "spreading" points of view, offering a number of examples in which they fail (See chapters 2.5 and 9.8). An example in which the dispersal idea fails is this: Consider two counter-rotating rings on a common axis, with equal but opposite angular momentum, separated by a small distance, each at, let's say, the same temperature. This is an equilibrium system. Now move the rings into contact with each other. Friction will slow and finally stop them. This will be an equilibrium system, both will be in contact, at rest, and at a higher temperature and entropy than the original two systems, yet there has been no spatial energy dispersal. PAR (talk) 18:10, 16 December 2020 (UTC)