Talk:Entropy/Archive 10

Major rewrite underway
I have started to rewrite this article. The information theoretic introduction will be kept, but the connection with thermodynamics will be made more clear right in the lead. The second law of thermodynamics, the fundamental thermodynamic relation will be written down explicitely on the lead. The advantage of the statistical approach is that all these statements come with explanations of how exactly they follow from the fundamental definition, so everything will be more clear.

I don't have the time to edit a lot every day. What I still have to do in the lead is explain why S can only increase, given the way we defined the entropy. Then we say that the way S depends on the external variables and the internal energy fixes all the thermal properties of the system. Then we define the temperature in terms of the derivative of S w.r.t. E, which leads to the relation dS >= dq/T.

We then have all the important properties explained heuristicaly in the lead, so lay persons can just read the lead and see the most important properties of S and read what follows from what and why. Count Iblis (talk) 01:06, 7 August 2009 (UTC)

Statistical thermodynamics
Hello, I am trying to make improvements to this article by incorporating references from Enrico Fermi but someone keeps deleting them without making any effort to incorporate them. These are viable calculations that clearly show the connection between Boltzmann's equation and the thermodynamic definition of entropy. I cannot understand why such contributions would be deleted when they address the key issue that this article wishes to consider. —Preceding unsigned comment added by Quantumechanic (talk • contribs) 02:04, 7 August 2009 (UTC)


 * The problem is that you cannot define entropy from thermodynamics alone. It is reverse logic and no modern textbook uses this approach anymore (with the possible exception of chemistry and engineering texts). Now, it used to be done like that (e.g. like in the book by Fermi, and Fermi, b.t.w., did not invent the thermodynamical derivations as you erroneously wrote in your version) but then you get a very complicated text that to engineers and chemists may look better (because they leaned it that way) but it actually doesn't explain one iota. What on Earth does the equation


 * dS = dq/T


 * really mean if you:


 * a) Have not explained what heat is?


 * b) you have not defined what T is?


 * Count Iblis (talk) 02:19, 7 August 2009 (UTC)


 * I agree. Certainly there is no reason to start from thermodynamics in this article if one can simply start from a more universal definition of entropy. Plastikspork (talk) 02:40, 7 August 2009 (UTC)


 * The disambiguation information states that this page is about entropy in thermodynamics. Your statement that "no modern textbook uses this approach anymore (with the possible exception of chemistry and engineering texts" is unsourced and unreliable.  Also your statement that "you cannot derive entropy from thermodynamics alone is unsourced and appears to constitute original research.  In short, there is a separate page for information entropy and that is where this information based material belongs.  In fact, I have multiple textbooks, which I can cite in the article, which develop entropy in a thermodynamics framework.  Hence, since this article is on thermdynamic entropy, there is no need to rely extensively on material belonging to another WP page.  Locke9k (talk) 01:20, 24 November 2009 (UTC)
 * You can certainly develop the concept of entropy via thermodynamics only, but then it is a purely phenomenlogical quantity that cannot be explained much deeper. Fortunately, the subject is not taught this way anymore to physics students. Also, obvious statements are not OR. It should be clear that thermodynamics alone cannot possibly tell you the number of microstates corresponding to some given macrostate. Count Iblis (talk) 02:10, 24 November 2009 (UTC)

The physical meaning of heat and temperature
Heat is energy. When we talk about entropy we are discriminating between heat that can do useful work and heat that is necessary to maintain the thermodynamic state (i.e. volume, pressure and temperature) of the system. Temperature is a measurement of the heat contained in an isolated system. For example, a given mass of aluminum at a particular temperature will have a specific heat capacity. That capacity corresponds to the amount of energy necessary to maintain that mass of aluminum at that temperature.

Quantumechanic (talk) 02:39, 7 August 2009 (UTC)


 * Temperature can be defined using the derivative of entropy with respect to energy. One can start by define entropy without defining temperature. Plastikspork (talk) 02:42, 7 August 2009 (UTC)


 * In addition, there is already an article on Entropy (classical thermodynamics). Plastikspork (talk) 02:44, 7 August 2009 (UTC)

OK, I'm giving it another edit but trying to stick with the more general definition of entropy. I hope you like this one better. —Preceding unsigned comment added by Quantumechanic (talk • contribs) 18:57, 7 August 2009 (UTC)


 * Sounds like a reasonable plan. Thank you. Plastikspork (talk) 23:20, 7 August 2009 (UTC)

Unjustified reverts
Now references to Fermi, Boltzmann and a recent work by Gardiner and Zoller have been deleted despite my repeated attempts to introduce new pertinent references and make this article read in a more encyclopedic style. Reverting from these additions is inappropriate unless the source material is bad or somehow misinterpreted. But the deleted source material substantiates those precise equations by which we have defined entropy in this article. Furthermore the mathematics by which the definition can be derived is clarified by these sources and additions.

It is my understanding that because these recent reverts have been deleting sourced material and replacing it with unsourced information, I am supposed to revert again. But before I do anything else I would appreciate feedback from anyone with an interest in improving this article. Quantumechanic (talk) 22:54, 7 August 2009 (UTC)


 * My only objection is to making the lead section unnecessarily dense with quantum statistical physics and thermodynamics terms. It would be great if the lead section could use a more general probabilistic definition of entropy, and then introduce the connections to quantum statistical mechanics and thermodynamics a bit further down.  This is, of course, my opinion. Thank you for your contributions. Plastikspork (talk) 23:18, 7 August 2009 (UTC)


 * Yes, the formalism using density matrices is welcome further down in the article. Most of the article is intended for people who don't kow the density matrix formalism. If someone knows about density matrices, then that person will very likely know a lot about thermodynamics. If such a person looks at this article, then it is most likely for technical stuff, e.g. about entanglement entropy etc. etc. So, the section you intend to write about that must have such a focus.


 * I don't think it is a good idea to focus too much about sources at this stage. Of course, we have very strict rules about what we write being sourced. But that is to keep crack editors away. The disadvantage of simply copying from textbooks is that you take a text on, say, page 400 of a textbook that is meant for students who have read through pages 1 to 399 and who have followed other physics courses (e.g. quantum mechanics). What we need to do is think about how we can best explain things to a, say, advanced high schooler who is very interested in physics and willing to spend some time to learn stuff. Count Iblis (talk) 00:54, 8 August 2009 (UTC)

It would be great to explain everything in as simple of terms as possible so we should work together to make the article as clear as we can. By pursuing an article that presents a statistical definition of entropy in the introduction we have the opportunity to enhance the article style if it is written in a clear and consistent manner. Our primary goal must be to the integrity of the article itself. Deleting viable sources defeats that goal.

If we choose to define entropy statistically and introduce the subject with respect to quantum states, mentioning the density operator in the introduction and the relationship between its simple diagonal form and its trace after the unitary transformation of interest helps clarify the equations being presented. I believe such clarification makes the article self-consistent. If we choose to go deeper into the matrix formalism of the entropy derivation within the article this will also be consistent. But a description of matrix mechanics is beyond the scope of this article.

The only other option I can see is to get rid of any mention of quantum mechanics from the introduction and focus on Boltzmann. Boltzmann's equation comprises a simple, statistical definition of entropy that can be introduced by his own reference. A reference to Fermi can also substantiate that Boltzmann did in fact prove his theorem. That way references to quantum optics texts could be resserved until later in the article. Quantumechanic (talk) 02:40, 8 August 2009 (UTC)


 * We could talk about "micro states" instead of "quantum states" in the lead. I think the lead should be as simple as possible, just sumarize the important properties of the entropy. In the next sections we'll give detailed explanations.


 * I don't really see the point in following sources very precisely. There is no point in saying that "S= k Log(Omega), see Boltzmann". You want to explain this (in your own words) first, and then you can can add the source. Also note that physics text should not be history texts.


 * The things that need to be put in the article are the equal prior probability postulate, an argument why entropy can only increase, the definition of temperature, the definition of work, the definition of heat, the second law. These things should be explained in a self consistent way in the article, not just dropped into the article with a source. Count Iblis (talk) 03:19, 8 August 2009 (UTC)

Request for comments
Now the introduction may be improved, but this article still needs a lot of work. Please let me know whether you think my efforts are consistent with our discussion. Also if anyone finds any mathematical errors please keep me apprised. I have not had time to check all of the equations yet but I will.

I decided to work on this page to hopefully give it more encyclopedic style. I would appreciate constructive criticism with respect to that goal. Also I recommend we take a critical look at the entire article and edit or remove any questionable content while taking care to preserve all pertinent sources and explain them better if necessary. Looking forward to your responses. Quantumechanic (talk) 23:21, 8 August 2009 (UTC)


 * I would suggest to move the stuff about the density matrix out of the lead to a later section. Just mentioning S = k Log(Omega) is enough. You then keep the lead section understandable for a, say, 16 year old high schooler. You can put the derivation of S = k Log(Omega) from a density matrix formalism in that later section.


 * About the next section on enthalpy: this is already covered in the wiki article on the Gibbs energy. The statement in this section comes with extra conditions: The system is in contact with a heat bath wich also maintains the system at constant pressure. I think that in the first section after the lead it would be more appropriate to consider an isolated system is more appropriate in the first section after the lead. You can simply set up the definition of the microcanonical ensemble in that section.


 * What we need to do in the first few sections after the lead is explain why the entropy will increase when you approach thermal equilibrium, how temperature is defined, the definition of heat and work (from the microscopic perspective), the steps that lead to the second law of thermodynamics etc. etc. Count Iblis (talk) 23:54, 8 August 2009 (UTC)

Those are good suggestions, Count. I realize that this article has some things to say about free energy but that there are already other articles on that topic. The same goes for entropy in information theory. I think that we should make an effort to consolidate various topics including enthalpy in the organization of the article. We should try to organize the article in a manner that makes it easy to read while building a conceptual understanding for the reader. Quantumechanic (talk) 01:36, 9 August 2009 (UTC)


 * I think you should change your writing style. Forget about sources and literal statements from books for the moment. I just read the section about enthalpy line by line (didn't do that yesterday) and it was completely flawed. You're text confuses free energy with actual work performed, you don't mention the conditions at which the statements that are correct are valid. Now enthalpy changes measure the heat supplied to the system (when pressure is kept constant), not changes in internal energy. Also the assumption tat processes be quasstatic was not mentioned, the whole notion of quasistaticity hasn't even even been introduced yet.


 * So, I had no choice but to delete that entire section on enthalpy. Count Iblis (talk) 15:57, 9 August 2009 (UTC)

I do not appreciate your deleting my work. It would be more constructive to help improve it. I am aware that we need to add a definition of the diagonal form of the density matrix to make the article more readable. But there is no need to delete viable equations and deleting good references is unacceptable. Each time you do that I am entitled to revert.

I disagree with you about the section on enthalpy. My writing assumes that the free energy is available to do useful work. I am trying to keep the discussion of free energy as simple as possible to avoid confusion. The important physics is that the work is done. If the system fails to make use of the available work, that is an engineering problem. But this is a physics article and not an engineering article. It should clarify the meaning of entropy. It is not intended to teach the engineering of a thermodynamic engine. Quantumechanic (talk) 16:57, 9 August 2009 (UTC)


 * It is perfectly acceptable to delete nonsensical texts. It nonsensical to start introducing entropy using a density matrix formalism, let alone without even defining what a density matrix is. Then, having started that way, the statement that Tr(rho log(rho)) is invariant is trivial, but you're then making some big point about that. And citation to an article on "quantum noise" instead of some basic text book is inappropriate. Count Iblis (talk) 17:07, 9 August 2009 (UTC)

Quantum Noise is a textbook. I am not aware of any basic texts that introduce a statistical definition of entropy in terms of the probability of states. Quantumechanic (talk) 17:10, 9 August 2009 (UTC)


 * Almost all textbooks I know do this. Count Iblis (talk) 17:21, 9 August 2009 (UTC)

Fixing the definition of entropy
I suggest that we change the first paragraph somewhat as follows, possible without the parentheses:


 * In thermodynamics, Entropy, usually denoted by the symbol S, is a physical quantity that is used to measure the internal energy of a system with respect to temperature. The entropy is related to the ability of the system to do useful work because it quantifies the heat energy internal to the system state that cannot do any work. The energy available to do work (free energy) is the difference between the total energy (enthalpy) and the internal energy (S T).

Please let me know what you think about this one. If the entropy is not clearly delineated from the free energy the definition is vague and ambiguous. Quantumechanic (talk) 17:48, 9 August 2009 (UTC)


 * Well, entropy is not "used to measure the internal energy of a system" at all. You can either give a definition that is really correct (e.g. the amount of information you would eed to specify the exact state given what we know about the system), or leave such more precise defintions fr later and then simply describe the way entropy is related to energy, heat and work.


 * In the second part fo your text, you write that entropy quantifies the eat content of the internal energy, but then must say that this is for a system ytat is kept at constant T. If you don't do that, then the relation is only valid for infinitessimal changes for entropy, as the temperature can change.


 * Another thing, I just say that in the last part of this article you editit in an integral expression of S involving Q(T). This looks strange to me and I'll check if this is correct right now. Count Iblis (talk) 18:02, 9 August 2009 (UTC)

Good points, thank you. Maybe this is better?


 * In thermodynamics, Entropy, usually denoted by the symbol S, is a physical quantity that is related to the internal energy of a system by multiplying the internal energy and the temperature of the system. The entropy is related to the ability of the system to do useful work because the heat energy internal to the system state cannot do any work. The energy that is available to do work (free energy) is the difference between the total energy (enthalpy) and the internal energy (S T).

I agree that those integrals look strange. I think it's a style issue mostly. The differentials look cleaner when lower case letters are used for the functions. But what was there before looked like it was edited by someone who doesn't know calculus. Quantumechanic (talk) 18:12, 9 August 2009 (UTC)

Let's see. You propose to write:

"S is a physical quantity that is related to the internal energy of a system by multiplying the internal energy and the temperature of the system."

Do you understand what you wrote here?

"The entropy is related to the ability of the system to do useful work"

Ok, so far. But this:

"because the heat energy internal to the system state cannot do any work."

doesn't make sense, because heat is not a thermodynamic state variable.


 * Technically you are correct because the internal energy does the work that puts the system into its state. So we really need to say that the internal energy cannot do any external work. Quantumechanic (talk) 19:02, 9 August 2009 (UTC)

Last part:

"The energy that is available to do work (free energy) is the difference between the total energy (enthalpy) and the internal energy (S T)."

This looks ok, if you say that this is for a system in contact woit a heat bath. In case of enthalpy, you look at a system that is kept at constant pressure (and volume pessure work against that system that keeps it at constant pressure then doesn't count as useful work). Count Iblis (talk) 18:29, 9 August 2009 (UTC)


 * It is true that most chemists are concerned with a reaction that occurs at atmospheric pressure and must account for changes in volume in terms of work done against the atmosphere. In this simple case the change in enthalpy is merely the heat absorbed in the process. When we talk about entropy we are actually more interested in what happens in a closed vessel where the pressure may increase as new components are introduced. Then the volume would be constant and no work is done against the atmosphere. Thus the change in enthalpy contributes only to the internal energy and no external work is done. But the enthalpy is still equal to the heat absorbed in the process.


 * Contrary to what you may believe, the work done against the atmosphere due to a change in volume of a chemical reaction does count as useful work. Of course only the free energy is available to be extracted. If you try to get more, the system will operate less efficiently and the pressure will end up above atmosphere. Quantumechanic (talk) 19:02, 9 August 2009 (UTC)

Integral expressions
I removed this edit:

Thus for a constant temperature process the derivative of the entropy with respect to heat is constant
 * $$\frac{dS} {dQ} = \frac{1}{T}.$$

If the temperature of the system is not constant, then the entropy must be integrated over both variables
 * $$S = \int {dQ} \int \frac {dT} T.$$

Since Q and T are mutually dependent in general, the integral becomes considerably more complicated
 * $$S = \int \int \frac {Q(T)} {T(Q)} {dQ} {dT}.$$

Comments:

A) Since when did Q get promoted to a thermodynamic state variable?

B) Ignoring point A) how do you get a double integral over T with integration measure "dT"? You could have replaced dQ by dQ/dT dT and gotten an expression in terms of a heat capacity, that would have made sense

c)Then in the last integral expression with Q(T), where did that come from? If you somehow integrate over Q (which you actually cannot do and the expression is flawed to start with), you would have lost one integral sign. Count Iblis (talk) 18:19, 9 August 2009 (UTC)


 * Consider an infinitesimal reversible transformation with entropy difference dS and an amount of heat absorbed dQ at temperature T. Thus
 * $${dS} = \frac {dQ} {T}.$$
 * that is substantially the first equation. If T is not constant the differential must be considered in two variables ie.e dQ and dT. That is why the integral gets more complicated. Quantumechanic (talk) 18:34, 9 August 2009 (UTC)


 * Ok, I think this provides the answer to the question I asked in the title of this thread beyond any reasonable doubt. Count Iblis (talk) 18:41, 9 August 2009 (UTC)

If you don't like the way I wrote down the integrals, why don't you suggest a way to fix them. I'm sure we can write the differential equation for the entropy when the temperature is not constant. Quantumechanic (talk) 19:07, 9 August 2009 (UTC)


 * Actually, I'm very glad with these integrals you wrote down. It settles the important question on how to proceed with editing this wiki article. Count Iblis (talk) 19:23, 9 August 2009 (UTC)

If you mean that we should edit out old stuff that doesn't make sense rather than try to preserve it and improve it, I agree. But I do not see a problem with writing the differential equation for the entropy when the temperature is variable. Why don't you suggest a form for that? Of course the integrals are fine now but they do not apply to a variable temperature process. Quantumechanic (talk) 19:43, 9 August 2009 (UTC)


 * I support Count Iblis' current version. It is clearer, more concise, and less "all over the place" than what was there before. As for a way to edit this article without unnecessary friction, I would advise QM to use (from this point on) multiple edits to make small incremental changes so that editors are not confronted with 1 massive change, but rather lots of smaller ones. It makes things easier to review, and if there is a problem with one, it does not invalidated all the rest of them. Headbomb {{{sup|ταλκ}}κοντριβς – WP Physics} 21:40, 9 August 2009 (UTC)


 * I concur. Part of the problem is that each edit looks like a massive rewrite when one looks at the diff. Plastikspork (talk) 22:10, 9 August 2009 (UTC)

Thank you for such valuable suggestions. Obviously I am a newb. But I can help make this article read in a more encyclopedic style, and maybe even make it more clear to the layman at the same time.

I feel that a clear and concise definition of entropy belongs right in the beginning. We have gone through both classical and quantum notions for such a definition. Regardless of which one we choose to maintain, we need to make sure that our assertions are adequately sourced for verification and further reading (and to keep with wiki policy).

Please give me more feedback so I can contribute most effectively. Thank you! Quantumechanic (talk) 22:39, 9 August 2009 (UTC)


 * Care to explain how those integral expressons you edited in this article were "sourced for verification and further reading (and to keep with wiki policy)" :(


 * You could have sourced your expressions or not source them, anyone who knows anything about thermodynamics knows that these expressions are wrong. So, you see that giving a source is irrelevant. It is only relevant when we're done writing this article and want to get this article to FA status. Count Iblis (talk) 23:03, 9 August 2009 (UTC)


 * An excellent source on the topic, IM(biased)O are Darrel Irvine's lecture notes on solid state thermo, available via MIT OCW. Right-hand column, click for annotated PDFs. Awickert (talk) 03:26, 11 August 2009 (UTC)

The introduction still doesn't make sense.
When the natural log is written in the entropy equation, Boltzmann's constant must be multiplied by ln 10. I suggest that we specify the logarithm in base 10 to fix this and clarify how Boltzmann's relation is related to the quantum mechanical description. Quantumechanic (talk) 00:25, 10 August 2009 (UTC)

The equations are incorrect when specified in the natural log. I think it is misleading to write Boltzmann's equation differently from how he originally expressed it, especially without correctly defining the constant. Furthermore the logarithm in the source material Quantum Noise is written with respect to base 10. It is derived from the Boltzmann relation and uses the same constant. Quantumechanic (talk) 01:04, 10 August 2009 (UTC)


 * What you don't seem to understand is that most editors here are experts in this subject. Then if you look in your book and see "log" and you see that we write "ln" then there are a few possibilties:


 * a) We are wrong (not just we here but other editors on other related wiki articles).


 * b) The book is wrong.


 * c) You may be mistaken that "log" always means "log in base ten".


 * The first reaction most people have when things don't seem to add up is check and double check if they themselves have made a error or a made an assumption that is not valid. If after checking and double checking and deriving the result ourself to get to the bottom of the matter, we have proof that the mistake is really not ours, and there is thus some anomaly (mistake in a source or whatever), do we raise the problem.


 * Your first reaction, not just now but from the first time you started to edit here was to make claims of errors in ths article right away without even attempting to provide for a detailed proof on the talk page (as indicated by some of your edit summaries).


 * There is nothing wrong when you write here about something that doesn't seem to add up. But constantly claiming that there is an error and that you have proof of that because you think that your source says something else than is written here, is just irritating. Count Iblis (talk) 01:22, 10 August 2009 (UTC)

I guess you're right. The book may be wrong unless (c) applies. (We already agreed that the normalized relation is a natural log.) So we need a better reference. And we need to explain it better. Boltzmann's relation teaches us about a collection of microstates in thermal equilibrium such that the lowest energy states are the most probable. If we explain it in terms of Boltzmann relaxation ratios we can clarify both the natural log and the minus sign. What do you think? Quantumechanic (talk) 15:38, 10 August 2009 (UTC)


 * Before we can explain the Boltzmann factor exp(-E/kT), we first need to explain the things that are explained in detail here. This section was written by me to provide for a first principles derivation that was missing in Wikipedia about a year ago. I have just made some small edits to the wiki pages on the first law of thermodynamics and on the page on work, in order to avoid circular definitions.


 * Now, in this article, we need to keep the very detailed math out, so we need to refer to other wiki pages were the things are explained. But that means that we may need to modify those wiki pages as well, if something is missing there. Count Iblis (talk) 16:05, 10 August 2009 (UTC)

The change in internal energy of a transformation that does useful work is important to the concept of entropy. We have already discussed some of the material in the article here especially about enthalpy and the first law. When we introduce entropy we can describe the physics in much more general terms. Free energy may be extracted from a variety of thermodynamic systems ranging from batteries to steam engines. So we shouldn't be limited to P, V systems in the general discussion of the first and second laws. Quantumechanic (talk) 16:45, 10 August 2009 (UTC)

Proposal: move equations out of lead
Now I looove math, but the average human being who wants to know about entropy may or may not have the background to deal with an analytical introduction to it. I suggest that: Awickert (talk) 04:09, 15 August 2009 (UTC)
 * The many disconnected clauses of the lead are combined into a coherent paragraph.
 * The mathy material is moved out of the lead (though still being described in words) or into a second paragraph
 * Sounds good. Plastikspork (talk)&#8202;―Œ 04:29, 15 August 2009 (UTC)


 * Yes, I agree. I think one could perhaps keep the equation k Log(Omega) with a statement that this is Boltzmann's famous formula that appears on his tombstone. I have been making small edits to the wiki articles on related subjects such as on heat, work and will make more substantial edits to the wiki article on the second law, before coming back here. This is to make sure that when we explain something here or in a related wiki article that you don't get a circular explanation like when you explain X in terms of Y and Z but then the wiki link to Y explains Y in terms of Z and X.  Count Iblis (talk) 13:13, 15 August 2009 (UTC)


 * OK, just FYI I am on vacation now and will be in the field this weekend, but I will be around again next week, and will be happy to help translate physics to English. Awickert (talk) 03:58, 16 August 2009 (UTC)

Expanded Second law of thermodynamics article
I have included a proof of the second law (I took it from the article on the fundamental thermodynamic relation which I wrote about a year ago). I do refer to this proof in the fundamental thermodynamic relation article on some other pages, so it should not be removed until the wiki links have been updated.

The proof starts from the relation S = k Log(Omega), so we can now write about the second law from the information theoretical perspective in this article and refer for the technical details to the second law article. Count Iblis (talk) 02:18, 16 August 2009 (UTC)

Information theory concept?
I believe the first section of this article was edited by somone from an information theory background, ignoring the rest of the article. Surely it can't be introduced as an information theory concept, when for decades it was purely a thermodynamic idea, then eventually applied in information theory? There is more than enough at the end of the article to explain the application of entropy as a concept in information theory. I also feel the start is written like a Batman vs. Superman argument. 192.198.151.37 (talk) 09:14, 17 September 2009 (UTC)


 * I agree. There is a separate article dedicated to the concept of entropy in information theory.  See Entropy (Information theory). Dolphin51 (talk) 11:58, 17 September 2009 (UTC)


 * I don't agree. Most modern courses on statistical physics explain entropy using a rigourous information theoretical approach or they do it more heuristically by introducing entropy as k Log(Omega). Definition of heat, work temperature etc. are all given in terms of the fundamental defintions. Only then do we discuss heat engines etc. in class. What we don't do is start wit heat engines, assuming that somehow temperature and heat don't need to be explained and then build up the theory. This is the historical approach and it is a recipe for disaster if you teach it this way. And, as explained here, this is true in general, not just in case of thermodynamics.


 * I do agree that the article needs a lot of improvement to explains things better. I started to work on this aticle last month, but I was caught up with more urgent matters on Wikipedia which has so far used up all the available time I can afford to spend here. Count Iblis (talk) 14:05, 17 September 2009 (UTC)
 * Entropy can't / shouldn't be introduced via heat? That doesn't sound plausible.  The 2nd law beomes almost trivial to explain.  Heat flows from the hotter to the cooler, hence dS=dQ/T > 0.  --Michael C. Price talk 17:55, 17 September 2009 (UTC)
 * Yes, but one needs to explain why the equation dS = dQ/T for reversible processes holds in the first place, see e.g. here. A big problem you face when you introduce entropy via dS = dq/T (not just introduce, but also build on it), is that the Second Law (that entropy increases) appeals on a notion of thermal equilibrium where you can define a temperature at all. But the fact that entropy increases is precisely due to non-equilibrium effects.


 * This problem is actually also mentioned in the criticism section of the second law article, which address the problems with the approach by Clausius. Count Iblis (talk) 18:36, 17 September 2009 (UTC)
 * I'm not saying that dS=dQ/T > 0 provides a proof, but it certainly provides an accessible explanation. --Michael C. Price talk 20:43, 17 September 2009 (UTC)

Assuming Count Iblis is correct, some strategic changes should be made. The present version of Entropy is clearly focused on thermodynamics and should be merged with Entropy (classical thermodynamics). A new version of Entropy should be created, based on the modern fundamental approach to entropy, and pointing towards each of the existing articles covering entropy:


 * Introduction to entropy
 * History of entropy
 * Entropy (classical thermodynamics)
 * Entropy (order and disorder)
 * Entropy (information theory)
 * Entropy in thermodynamics and information theory
 * Others listed at Entropy (disambiguation)

The present version of Entropy is clearly based, almost exclusively, on the classical thermodynamical perspective of entropy. It has an image of ice melting in a glass of water; it has an image of Rudolph Clausius; and many references to heat and temperature and thermodynamics. But the opening paragraph is an incongruous and incompatible reference to information theory. Dolphin51 (talk) 23:19, 17 September 2009 (UTC)
 * There should be separate articles for each of the main types of entropy. Sticking it all in one article is too much.  The main article can just talk about how the different concepts relate to each other. --Michael C. Price talk 21:50, 18 September 2009 (UTC)

New Synthesis?
I am relatively new to Wikipedia and have made some significant changes/additions to the beginning of this article in the past two days. My purpose is to synthesize and summarize the three opposing viewpoints so that each of their strengths can work together (instead of opposing each other and confusing the curious). Admittedly, I focus more on the microscopic/information viewpoint than the macro/thermo viewpoint. However, I tend to learn and explain more pedagogically than mathematically, which is why I use equations sparingly. I am open to suggestion, critique, criticism and conflagration in effigy. I am not an expert on the subject, merely a BA in chemistry whose favorite courses were P-chem and quantum mechanics. But I feel that I have a reasonable grasp of this important concept. Am I wrong?

There have been few changes to my edits and I am looking for some feedback. There seems to be a lot of vitriol on this page, but I think that we can all work together and get along (and hopefully get back on the featured article list). One problem I currently have is that the fourth paragraph is very disjointed from the first three, which I have been working on. But I don't want to delete the concepts. Perhaps someone can insert a better segue.

--User:Kpedersen1  20:28, 4 October 2009 (UTC)


 * I think you did a great job. I think the rest of the artcle should now be rewritten to bring it firmly in line with the information theoretical introduction. The connection between thermodynamics and the fundamental definition of entropy should be made clear. We could start with the temperature. The definition 1/T = dS/dE can be easily motivated when you consider two initially isolated systems each with their own Omega(E) function.


 * Then, I think some statements that are now made in the lead about the universe, the S T_R energy associated with information content should be explained elsewhere in the article in more detail. Maxwell's Demon and Laplace's Demon can be introduced to illstrate the relevance of information in thermodynamics in a less abstract way. Formula's for entropy, like Sackur Tetrode's formula for the entropy for an ideal gas could be given. Count Iblis (talk) 21:15, 4 October 2009 (UTC)


 * Feynman Lectures on Computation have an excellent chapter on the thermodynamics of computation, bit : k log 2 connection, why resetting bits takes energy and how Bennet's machine can run on bits. --Dc987 (talk) 08:47, 20 October 2009 (UTC)

Information Concept First
A recent edit dropped in the thermodynamic definition of entropy as the first sentence (thank you for fixing it Count Iblis). I think this thermodynamic definition is very important, but should not be introduced until later in the article - certaintly as the main concept in the thermodynamic approach section. I understand the frustration of thermo people who see the information concept introduced first, since it was developed later. But given what we now know about entropy, the information concept is a more foundational approach. In quantum mechanical systems, entropy is explicitly defined as information. (The Black hole paradox deals with the thermodynamics of a black hole, but defines the 2nd law as "information cannot be destroyed in the universe"). Thermodynamic systems are composed of quantum mechanical ones; thus thermodynamic entropy is an emergent property of informational entropy. Certaintly thermodynamics has more importance on our daily lives, since we generally deal solely with the classical limits of quantum mechanical laws, but a true undestanding of any physics must begin with its physical origins (not its intellectual ones).

Therefore I think the introduction section should deal almost strictly with microstates, information, and the entropy defined as the potential for disorder (and, alternatively, the amount of information needed to descrive a system). Once this ground is covered, we can delve into how this affects the amount of useful work a system can perform, entropy changes of phase transitions, entropy of mixing, etc. and how these can be traced back to entropy as information. Hopefully if we all work together and embrace the duality of entropy as energy and information, we can get this very important page back on the featured article list. If you have objections, please discuss them here so that we can compromise before slashing and burning the hard work of others (I have been very careful not to remove any ideas in my edits, at the very most rephrasing them and re-organizing their structure). Kpedersen1 contributions (talk) 10:22, 9 October 2009 (UTC)


 * There is no such thing as duality of entropy. Lookup the Landauer's_principle and Entropy_in_thermodynamics_and_information_theory. --Dc987 (talk) 08:37, 20 October 2009 (UTC)

Cosmic inflation and entropy: please expand
Would someone expand the section which reads, "The entropy gap is widely believed to have been originally opened up by the early rapid exponential expansion of the universe"? It needs sources to start with. Also, did expansion open a gap because when distant stars and planets become unobservable, their entropy contribution no longer counted and the observable universe decreased in entropy? Or was there solely an increase in the total possible entropy of the universe? If so, was this because the universe cooled down and more kinds of broken symmetry (like atoms and molecules) became possible? Or was it because there was just more space for particles to be distributed in? I'm sure there are some egregiously wrong-headed questions in here - ruling them out may be a way to begin adding more content to the article. Wnt (talk) 07:09, 21 November 2009 (UTC)

Greem etymology
I know this sounds a bit trivial, but still.. :P

Do you think this section:

(right above the TOC)

should be placed, in a shortened form, right next to the first instance of the word "Entropy" in the very beginning of this article? That's how it's usually done with other scientific/philosophical/psyhological/whatever Greek/Latin/etc-derived terms (e.g. Dynamics, Logos etc), and I think it makes more sense to be right where the word is found for the first time rather than somewhere else in the page. Something like " Entropy (from the Greek εντροπία, "a turning toward")[4] " maybe..

Sounds good? • jujimufu (talk) 10:51, 23 November 2009 (UTC)

Focus of this article
It seems to me that this article is presently off point. We have an article on Entropy (information theory). This page is stated to be on "entropy in thermodynamics". Nevertheless, the focus of the introduction is on information entropy, and there is considerably discussion of that topic in this article. This article needs to be refocused on the material that it is purportedly on based on the disambiguation information: thermodynamic entropy. Whats more, having a very technical article and a redirect to an "introduction to entropy page just really isn't the right way to do things. I am sure that this article can be written in a way that is initially clear to the layperson or at least generally technical person, and then progress into more technical material later.  Furthermore, I am sure that material on information entropy will benefit by being moved to its existing, dedicated page.  I will thus begin to make edits in these directions. Locke9k (talk) 00:36, 24 November 2009 (UTC)


 * There is Classical thermodynamics (1824) and Statistical thermodynamics (1870+). It seems to me that you are trying to move the article towards the 1824.--Dc987 (talk) 10:36, 25 November 2009 (UTC)


 * I'm not clear what you mean exactly. I think that the reworked intro clearly reflects the statistical thermodynamic view of entropy, as well as the classical view.  The only thing I am trying to move the focus away from is information entropy, which is actually a separate (although related) topic and was being made the focus of parts of this page.  I think that its very important to cover both the classical and statistical mechanical views of entropy within this article, as its not really possible for a lay person to get the complete historical and physical view of entropy otherwise.  Also, I don't think that these two viewpoints are in any way competing, but are rather complementary.Locke9k (talk) 16:45, 25 November 2009 (UTC)

Original research
Various parts of this article are uncited, dubious, and seem likely to be original research. I am removing such material and where it seems useful I am copying them to this page. Please do not readd them to the article without citation. Following is the first such section.

"The true importance of entropy and the second law can be understood by altering the second law in a "toy universe" and studying the implications. Given the knowledge we now possess about atomic/quantum theory, it is no stretch to generalize all universal phenomena as "particle interaction". If the second law required entropy to remain constant, then particle behavior would be limited so as not to increase the balance of interacting systems (new interactions would only be allowed if they terminated old interactions). The universe would either be static or strange. And if the second law were reversed (total universal entropy decreased with time) then particle interaction would either require a certain amount of particle combination (annihilation of sets of particles into smaller sets) or interaction itself would be required to diminish. However, this does not mean that the second law bestows absolute freedom of interaction; total universal entropy must still increase with any physical process. Thus the spontaneity of any physical process can be predicted by calculating its $$\Delta S$$ (the more positive $$\Delta S$$ is, the more probable the process is). "

Locke9k (talk) 04:13, 24 November 2009 (UTC)


 * Sounds like a MaxEnt approach. --Dc987 (talk) 20:36, 24 November 2009 (UTC)

Deck of cards analogy
All states in the deck of cards are equally likely. So why specify any one state to start and then declare that another state is more randomly arranged on shuffling. I have seen this before and doubted it then; no specific state has any more combinations than one, the same number as the starting state. —Preceding unsigned comment added by Quaggy (talk • contribs) 18:01, 30 November 2009 (UTC)


 * What is left out in the text (in order not to make it technical, I presume), is that you need to count the number of microstates consistent with a certain macrostate. In this case we distinguish between a decks of card for which we do not have any information about how it is aranged and decks of cards for which we a priori know that it is arranged in some neat ordered way. These two types of decks of cards have to be considered to be different macroscopic pobjects.


 * The entropy is then the logarithm of the number of ways you can re-arrange the cards such that it would still be the same macrostate. Now, what a macrostate is, is matter of definition (in practice we make a choice that is the most relevant from an experimental point of view). In this case we can define two macorstates corresponding to the deck of cards being ordered or not ordered, but you can choose an alternative definition in which you do not make any such distinctions. Count Iblis (talk) 18:21, 30 November 2009 (UTC)


 * I think the present example, although Count Iblis is strictly correct, is not the best. I think it would be better to define, for example, a macrostate where all the black cards are on top, all the red cards on the bottom. Then we could talk about the number of microstates that correspond to this macrostate. That might be enough, but then we might make the intuitive argument that a macrostate where no five cards in a row were the same color would be a macrostate that had more microstates, and therefore more entropy than the first macrostate. PAR (talk) 00:34, 1 December 2009 (UTC)

Confusing statemnt
From the lead:


 * "Increases in entropy correspond to irreversible changes in a system"

From a layman's standpoint this is clearly not true. Taking the melting-ice example in the graphic, the ice can be re-frozen. Does it mean irreversible without expenditure of energy perhaps? My competence in the subject is not sufficient to make any changes. 81.129.128.164 (talk) 22:01, 1 January 2010 (UTC).


 * This is the case for an isolated system. If you put ice in hot water in a container that is completely isolated from the environemnt, then the ice will melt. To get the initial state back requires you to let the contents of the container interact with the environment. If you do that, you can look at a larger volume that consists of everything the container has significant interactions with. The entropy of that larger volume will increase because it is approximately an isolated system. Count Iblis (talk) 00:05, 2 January 2010 (UTC)


 * Right, thanks, I think I understand you. I recommend that this is clarified in the article. For people without this specialist knowledge of the conditions pertaining to "a system", the statement appears not to make any sense. The rest of the sentence is not easy to understand either: "... because some energy must be expended as waste heat, limiting the amount of work a system can do". I have no idea how or why this "because" follows. I realise that this is a difficult subject, and I also realise that there is a "generally accessible and less technical introduction" elsewhere. Even so, for someone coming to Wikipedia and looking up "entropy", the sentence I'm complaining about is practically the first thing they read, so anything that can be done to make it easier to understand is a good thing, in my opinion. Thanks again for your explanation. 81.129.128.164 (talk) 01:29, 2 January 2010 (UTC).


 * A further thought. If I have this correct now, even in an isolated system, any given entropy-increasing change is not irreversible. Anything can be reversed, provided something gives (entropy-wise) somewhere else. So, "Increases in entropy correspond to irreversible changes in a system" seems misleading, even if the point about the system being isolated is clarified. 81.129.128.164 (talk) 02:31, 2 January 2010 (UTC).


 * What happens in system A will be completely independent of what happens in system B, unless system A and B can interact. So, if it is the case that there is an entropy decrease in system A is allowed because the entropy in B increases by a larger amount, then there would have to be interactions between A and B. I agree with your previous comment that we should explain things better in this article.Count Iblis (talk) 23:39, 2 January 2010 (UTC)

Entropy vs Chaos
I've heard mention in talking with some physicists that even though Entropy is counted as Chaos in a small closed system, the act on a universal scale it would be more accurate to describe entropy as a movement towards order... in otherwords, the heat death of the universe would result in the closest thing to absolute predictability of the universe. However, I'm unable to find what I would consider a good citation for this. —Preceding unsigned comment added by Starfyredragon (talk • contribs) 21:13, 3 November 2009 (UTC)
 * Weird thing for them to say, since the heat death has maximal heat released and heat, by definition, is unpredictable.--Michael C. Price talk 02:16, 5 November 2009 (UTC)


 * Equating entropy with disorder or chaos is a little simplistic and not always true. If you think about diffusing atoms in a gas, disordered microstates are much more common than microstates that have a structured arrangement of atoms.  However, if you look at closed systems with attractive forces at work (like gravity or chemical bonds) increasing entropy can be associated with increasing structure.  For example, the growth of a crystal or the gravitational collapse of a gas cloud into a solar system of planets represent increasing entropy. DonPMitchell (talk) 06:59, 28 February 2010 (UTC)

Measure of Entanglement
Entropy is a measure of entanglement. [] And entanglement is not even mentioned in the article. Not even once. --Dc987 (talk) 08:22, 20 October 2009 (UTC)


 * I assume that you mean "entanglement" in the rigorously-defined, quantum mechanical sense (c.f. Einstein, Podolsky, and Rosen). Perhaps the most powerful aspect of classical thermodynamics is that is independent of the specific formulation of statistical mechanics which gives rise to it as an emergent mathematical framework; as such, the definition of entropy exists completely independently of entanglement (as implied by the applicability of the entropy concept to information theory). Reference to entanglement is therefore unnecessary. If you think that a subsection on this is appropriate, find some external resources and write the section. Calavicci (talk) 19:38, 1 November 2009 (UTC)


 * I'm not sure if any definition that doesn't mention the entanglement part would be a complete definition, not just a classical approximation. The article already has the subsection on entropy in QM: []. But it is technical. And it doesn't mention the entanglement part. The main article on the Von_Neumann_entropy does:
 * Intuitively, this can be understood as follows: In quantum mechanics, the entropy of the joint system can be less than the sum of the entropy of it's components because the components may be entangled. For instance, the Bell state of two spin-1/2's, $$| \psi \rangle = | \uparrow \downarrow \rangle + | \downarrow \uparrow \rangle $$, is a pure state with zero entropy, but each spin has maximum entropy when considered individually.  The entropy in one spin can be "cancelled" by being correlated with the entropy of the other.
 * --Dc987 (talk) 23:02, 4 November 2009 (UTC)


 * A definition of entropy without mentioning entanglement is, indeed, complete. The idea is that entanglement is only one of any of the numerous properties of systems which can lead to entropy when analyzed statistically. Entropy is not dependent on entanglement to exist. Trying to incorporate it in the definition is trying to define an abstract concept with a concrete example, like defining a derivative by saying that velocity is the first derivative of position with respect to time.Calavicci (talk) 21:06, 6 December 2009 (UTC)


 * "Entropy is not dependent on entanglement to exist." - I wouldn't be so sure about that. If you consider the QM definition of entropy, the density matrix pretty much specifies the entanglement between the system and the observer. --Dc987 (talk) 06:28, 8 December 2009 (UTC)

But entanglements can be reversible, whereas entropy is not. Suggests entropy is not a measure of entanglements, but only of irreversible entanglements.--Michael C. Price talk 19:50, 1 November 2009 (UTC)


 * Er, you can either use entropy to quantify the entanglement between two systems or you can not. You can. So it entropy is a measure of entanglement. The opposite is not necessarily true, but either way, entanglement is an important part of entropy and I think it should be mentioned in the article.
 * Offtopic: Speculatively, physical entropy and the second law can be a consequence of entanglement and decoherence, but I don't think it is an established fact. IMHO to discuss the reversibility you need the time arrow, and this arrow would point backwards if you reverse an entanglement (if you really reverse it, not just leak to the environment); but it's not really relevant here. --Dc987 (talk) 23:02, 4 November 2009 (UTC)
 * Your use of entropy as a measure of entanglement violates the 2nd Law, where the entanglements are reversible.--Michael C. Price talk 02:13, 5 November 2009 (UTC)
 * Er, it is not me, who uses entropy that way. See: ,
 * Continuing Offtopic: Not really. Reversible by definition implies that the arrow of time is pointing backwards. And the 2nd Law only requires the increase of entropy in the direction of the arrow of the time. BTW. Can you give an example of reversible entanglement?
 * --Dc987 (talk) 05:57, 5 November 2009 (UTC)

There are two statements: 1. Entanglement entropy merely one of the contributions of the whole entropy; 2. The whole entropy equals the entanglement entropy;

I understand that the first statement is a well established fact. Second statement is a speculation. --Dc987 (talk) 05:57, 5 November 2009 (UTC)


 * I think the relation between entropy and entanglement is useful to discuss in this article after we finish rewriting the first few sections. Perhaps some easy to understand example involving qubits states can be used to explain it. Count Iblis (talk) 14:31, 5 November 2009 (UTC)


 * About reversibility, in principle everything is reversible (at least, assuming unitary time evolution). The reason that entropy can increase is because we don't look not at a picture of the system, but instead at a coarse grained picture of the system. I think that entropy in QM can be formally defined just like in the classical case, the only difference is that you have to replace "bits" by "qubits". This then automatically includes all the subtleties caused by entanglement. But to be sure, I'll look it up. Count Iblis (talk) 14:39, 5 November 2009 (UTC)


 * Hehe. You've mentioned "easy to understand" and "qubits states" in the same sentence.
 * Yes, entropy in QM can formally be defined just like in the classical case; I think that Von Neumann definition does it. The trouble with this definition is that $$ S(\rho) \,=\,-{\rm Tr} (\rho \, {\rm ln} \rho),$$ takes a lot of effort to take in. While a few example involving a couple of electrons are very intuitive. --Dc987 (talk) 20:32, 5 November 2009 (UTC)

This whole discussion is somewhat missing the point. We can define a quantum mechanical entropy such as the von Neumann entropy for a quantum system. It should be noted that this, as given, is more an entropy in the sense of information theory than in the sense of thermodynamics, although the two are strongly related concepts. However, entropy (or, to be pedantically precise, quantities all of which we address by the single term "entropy" because they behave in the prescribed manner) arises in a vast number of systems which are described by mathematical models which are very different on the level of statistical mechanics. If quantum mechanics did not exist and the universe were classical (This is false, but that does not change the succeeding point.), entropy would still exist and behave as it does. Nature could have chosen a fundamentally different form for physics and given rise to an entropy which behaves just as ours does — i.e., an entropy which is identical, in all (thermodynamically) meaningful ways, to ours. Moreover, we can both calculate entropy and calculate with entropy in a purely macroscopic way. Entropy itself is neither a classical nor a quantum-mechanical concept; it is a more general one which parameterizes our ignorance of thermodynamic systems. As such, it is not necessary to a (thermodynamic) discussion of or definition of entropy to go into the details of the particular (quantum, or classical for that matter) statistical mechanics which gives rise to it; it may, however, be useful to include a discussion of how we apply the concept of entropy to quantum systems, including the relationship to entanglement, and what this means. If and when such a section is written, we should treat the quite subtle distinction between quantum information entropy and thermodynamic entropy carefully, although I would not be qualified to describe this distinction without a little background research.

Moreover, there seems to be some implication here that entanglement, in some metaphysical sense, somehow "gives rise to" entropy; i.e., that entanglement is a fundamental quantity and that entropy is our way of parameterizing it for study. If that is the way that we wish to view entropy (and there is some justification for that point of view, in the senses of information theory, both abstract and quantum, and thermodynamics, although the very question of "how to view entropy" it is probably more philosophical than scientific), then the fundamental quantity is really probability, and entanglement itself is a property of how the probabilities of composite quantum systems behave.

There definitely seems to be enough interest in the link between entanglement and entropy to include something on it in this article, but we should not characterize entanglement as "the" thing which entropy characterizes or measures. We should explain that there is a profound connection between the two, probably in an elaboration of the section on von-Neumann entropy. To adopt the latter approach would be enlightening of us, but to adopt the former would be fundamentally incorrect of us.

Calavicci (talk) 10:58, 21 March 2010 (UTC)

External vs Extensive variables
External variables relate to conditions outside the system, in the surroundings, while extensive variables are those that are not the bulk physical properties of the system. Extensive variables are mass, volume etc. while intensive variables are density, temperature, viscosity etc. The ratio of two extensive variables is an intensive variable and is scale-invariant. See Intensive and extensive properties. I've changed any improper use of external variables to extensive variables Larryisgood (talk) 13:57, 3 May 2010 (UTC)


 * What is meant here is what F. Reif calls "external parameters", and I'm sure all statistical mechanics textbook will call them external parameters or external variables. These variables don't need to be extensive. It refers to variables that specify the macroscopic description of the system. The reason why one refers to them as "external" is because controlling the system so that it has prescribed valus for the variables, requires imposing constraints which requires interaction with an external agent.


 * Note e.g. that the derivative of the energy w.r.t. the extensive external variables at constant entropy will yield the conjugate forces (e.g. pressure in case of volume). Count Iblis (talk) 15:49, 3 May 2010 (UTC)


 * Sorry, maybe i should have left a bit more time on the discussion page before i jumped the gun and changed it. I know at least that in Thermal Physics - C.B.P. FINN such parameters are referred to as extensive variables. Perhaps it's a difference in nomenclature between classical and statistical thermodynamics? Larryisgood (talk) 21:21, 3 May 2010 (UTC)

I wish I knew how to add things to my own comments
My mistake on that one, haha. I overlooked the part where the article explained heat transfer from the body was positive (every class I've ever taken has had it as negative). That's why I'm used to seeing the Inequality with a less than or equal to sign. Thanks again! —Preceding unsigned comment added by 24.3.168.99 (talk) 06:45, 23 November 2007 (UTC)


 * This is really important and sometimes confusing. I've also seen the inequality for negative convention of heat transfer, so it was less than or equal. nihil (talk) 05:59, 19 May 2010 (UTC)

Energy Dispersal
This gives the false impression that the concept of "disorder" is no longer used in mainstream introductory chemistry classes. However: “Entropy is actually a very easy concept to think about. It's a measure of disorder. I think most of us have a very good concept of how things tend to go to disorder, so it's something we can conceptionalize in an infinitie number of ways. Entropy is simply a measure of the disorder of a system, And when we're talking about chemical reactions, what we're talking about is a change in entropy, so whether as a reaction goes forward, are we becoming more ordered or more disordered.” - Professor Catherine Drennan, MIT, Principles of Chemical Science, Video Lectures, Lecure 17, Topics Covered: Entropy and disorder, quote occurs at 25:40

The statement that "Peter Atkins...has discarded 'disorder' as a description", appears to be slander against Professor Atkins. If you google "Peter Atkins Physical Chemistry entropy disorder", you will find, on Google books, Elements of Physical Chemistry by Peter Atkins and Julio de Paula, 2009,Page 86: "It should be plausible that the change in entropy - the change in the degree of disorder - is proportional to the energy transfer that takes place by making use of disorderly motion rather than orderly motion . . . . a hot object (one in which the atoms have a lot of disorderly thermal motion) . . . . The entropy is a measure of the current state of disorder of the system . . . . A sample . . . has the same degree of molecular disorder - the same entropy - regardless of what has happened to it in the past" Page 87: "the entropy of a sample gas increases as it expands because the molecules get to move in a greater volume and so have a greater degree of disorder." —Preceding unsigned comment added by Ray Eston Smith Jr (talk • contribs) 20:48, 10 July 2010 (UTC)


 * You are correct that Atkins uses different approaches in different books, but it is not a slander. He certainly uses the idea of energy dispersal in editions 8 and 9 (2010) of "Physical Chemistry" which was his first book and is clearly his flagship book on physical chemistry. I have made a small change to that paragraph that I believe clarifies it. -- Bduke   (Discussion)  23:50, 10 July 2010 (UTC)


 * This definition "According to the second law of Thermodynamics, entropy is a measure of the energy which does no work during energy conversions" could be more precise.Nobleness of Mind (talk) 13:44, 18 July 2010 (UTC)


 * You can read the story or rather history of the energy dispersal textbook-change debacle here:


 * Energy dispersal


 * --Libb Thims (talk) 17:12, 18 July 2010 (UTC)