Talk:Gibbs paradox

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[edit] Suggestions

Feel free to change my version. I have fun with Gibbs paradox. Best regards,--Linshukun 20:10, 3 November 2007 (UTC)

I worked on this paper today. It looks better. The references can be added to the text more precisely and listed at the end in a better way. The section of von Newmann's "Quantum Mechaniccal resolution of Gibbs paradox" must be expanded.Linshukun 09:33, 28 October 2007 (UTC)

I deleted "...known as mixing paradox". I have never heard of this word "mixing paradox" among people publishing on Gibbs paradox. Let us continue to say "Gibbs paradox" to remember Gibbs, one of the greatest American scientists. Linshukun 20:56, 27 October 2007 (UTC)

The section "Calculating the Gibbs paradox" should be deleted. This is merged to the other section. Linshukun 20:43, 27 October 2007 (UTC)


The phrase "Gibbs Paradox" has a specific historical meaning that deserves a short, standalone, reference article based on a standard reference source. For an online version of such a reference see this on Mixing Entropy and Gibb's Paradox from MIT's OpenCourseWare lectures on basic thermodynamics and statistical mechanics. While I appreciate LinShuKun's ideas and interest in this topic, I believe that his ideas and the ideas of Jayne's belong in a separate article; perhaps "Current Topics in Mixing Entropy" would be an appropriate title. Mixing these not-yet-widely-used ideas with such a well-established concept violates the principles of neutral point of view and no original research. This is a great example of why these principles exist: as the article currently stands, a non-expert reader cannot distinguish which ideas are the historical topic of Gibbs Paradox and which ideas are new. The new ideas deserve a separate article. jrf 21:18, 15 April 2007 (UTC) Agree with you: "Current Topics in Mixing Entropy" can be set up.Linshukun 09:33, 28 October 2007 (UTC)

I believe that the 'Gibbs Paradox' article SHOULD NOT be merged with the 'Mixing Paradox' article as Gibbs Paradox can be used outside of a scientific context. To merge the two articles suggests that it must be confined to a scientific scenario.

I am happy with both articles, however I would suggest that the 'Gibbs Paradox' article be positioned into a more understandable context. HarryPellegrini 13:01, 7 May 2007 (UTC)

[edit] Category - Quantum mechanics

Gibbs paradox is resolved through the introduction of Planck's constant, or at least the quantization of phase space, resulting in the Sackur-Tetrode equation. PAR 11:46, 13 May 2005 (UTC)

If the question is wether the article should be also in the category "qm", then I completely agree with you. Please go ahead :-) -- mkrohn 11:49, 13 May 2005 (UTC)

[edit] Dimensions

The number of states φ / h3, of which one takes the logarithm to get the entropy, has dimension (mass × length / time)-1, since the dimension of the constrained phase space is lenght3N×momentum3N-1 and not lenght3N×momentum3N . Shouldn't this be made dimensionless somehow? --V79 22:17, 15 October 2005 (UTC)

Good point. Talking about the "area" of the cylinder wall is bad form, it has zero volume, in contradiction to the idea that you can't specify a volume smaller than h^3N. I fixed it in a hand-waving kind of way, but maybe it needs to be more fully explained. PAR 00:24, 16 October 2005 (UTC)

[edit] No paradox, and no need to introduce indistinguishability of particles

Actually the "resolution" of the Gibbs "paradox" as described here, even though standard, is not correct. If you look at the thermodynamical definition of the entropy you will see that 1) it is defined up to an arbitrary function of the number of particles, and 2) there are no a priori reasons to assume it should be extensive (and it is actually not extensive in systems with long-range forces, e.g. gravitational systems). I don't want to enter into too much details here, since all of this is perfectly explained in a beautiful paper by Jaynes, available at this address :

http://bayes.wustl.edu/etj/articles/gibbs.paradox.pdf

Please have a look. One should at least mention this and cite this paper. There is no paradox, and no need to introduce indistiguishability of particles (for this particular problem).

Well, I started out thinking this was another crackpot paper written by someone who went off their medication, but its not. This is an EXCELLENT article. I always had a sneaking suspicion that I didn't really "get" entropy, and now I feel better, because I realize that nobody does, except maybe Gibbs and Pauli. I also thought this might be a dense, impenetrable article, but the whole point of the article is that this guy Jaynes is trying to make sense of some of the impenetrable writings of Gibbs. That means he is very dedicated to clarity, and for anyone who took college thermodynamics and statistical mechanics, and more or less got it, this is a pretty clear article. Which is not to say I understand it on first reading, its going to take a number of iterations. Thanks for that reference, and we should be able to incorporate these ideas into a number of wikipedia articles, since they are not so much "revolutionary" ideas, but rather a realization that certain (published!) insights of giants like Gibbs and Pauli have not made their way to the mainstream. PAR 18:57, 2 November 2005 (UTC)
I am happy that you like it. Actually, I also recommend most of the other papers he has written, many of which deal with entropy (including his celebrated 1957 Phys. Rev. paper, in which he provides foundation to statistical mechanics based on information theory - much, much better than the ergodic approach, in my opinion; see also his more recent contribution to this topic). All his papers can be found at the same place,
http://bayes.wustl.edu/etj/node1.html
All these papers are written in the same very clear way, and many professional statistical physicists (and probabilists) would profit from reading them. --YVelenik 08:51, 3 November 2005 (UTC)
Well, I think it is really a pity that these clearly wrong claims (that 1) there is a paradox, and 2) it is resolved by postulating indistinguishability of particles) not only remain here more than 5 months after my first comment, but that the article actually is getting worse in this respect. I don't want to spend time giving convincing arguments for my claim, since this is done, and very well, in the paper I cited above... I would like to think that people interested enough in these topics would be curious enough to read it (or at least browse through it)!

--YVelenik 16:47, 21 April 2006 (UTC)

I have not looked at the article for a while, but now that I do, I agree. Lets fix it. I do, however, think we need to respect the conventional paradox, and explain its origin, before introducing Jayne's analysis. Note that I entered Jaynes explanation of Gibb's explanation of the mixing paradox in that page. PAR 17:13, 21 April 2006 (UTC)

[edit] Disputed

The density of states is wrong by a small, but significant factor. Anyone have an authoritative reference?

I think "Statistical Mechanics" by Huang contains the derivation, and I will include it as a reference, but I have to make sure it agrees. How would you write the density of states? PAR 01:54, 19 January 2006 (UTC)
The correct answer is, I think,

g(E) = \frac{1}{ h^{dN}} \cdot \frac{V^N}{N!} \cdot \frac{(2 \pi m )^{\frac{dN}{2}} }{\Gamma(\frac{dN}{2} )} \cdot E^{{\frac{d N}{2}}-1} 'd' is the spacial dimension.

[edit] too technical tag

i removed the tag. since there's a "context" tag on the article itself, it seems redundant. if you want, go ahead and reinsert the tag, but please leave some specific suggestions about what you think the article needs. thanks. Lunch 04:43, 24 September 2006 (UTC)

[edit] RFC: Review of new material requested

There has been an enormous amount of material inserted into this article, primarily by one author, which includes reference to the author's own work. I would like people skilled in the field to review and verify that everything is OK.Kww 01:59, 2 November 2007 (UTC)

This does not look OK to me. It begins with messy definitions and proceeds to voodoo similar to voodoo that's often used to equate information theory with real particles. Nearly every sane physicist, engineer, thermodynamicist, and child is perfectly comfortable with discontinuities in the physical world when undergoing the mental transition from microscopic to macroscopic thinking. Here's ice. Here's liquid water. It takes an information scientist to imagine a nice linear range of values between the two that can be plotted on the x-axis of a chart to make it seem like something paradoxical is taking place.
Ben-Naim's paper looks OK to me. It says "for ideal gases, the mixing, in itself, does not play any role in determining the value of the so-called entropy of mixing. Once we recognize that it is the expansion, not the mixing, which causes a change in the entropy, then the puzzling fact that the change in entropy is independent of the kind of molecules evaporates." In other words, with a barrier being removed in gas A, you begin and end with two volumes of A. With a barrier removed between two separated gases, you begin with one volume of A and one volume of B and you end up with two volumes of diluted A and two volumes of diluted B. The word "expand" or "expansion" doesn't appear in the present version of the article anywhere, and the word "volume" doesn't appear in the classical thermo section. Instead, it says, "The fact that the different gases have mixed does not yield a detectable change in the state of the gas." Wrong, wrong, wrong. It does yield a detectable change (increase in volume, decrease in concentration) in the state of two gases, so it yields a detectable change in the state of the gas as a whole. Ben-Naim goes on to write: "The fact that entropy changes discontinuously as one changes the indistinguishability continuously, is viewed as a paradox. However, there is no paradox here, and there was no allusion to any paradox in Gibbs writings. There are many examples that a discontinuous transition follows a continuous change of a parameter. For instance the fact that the density of water changes discontinuously when the temperature changes continuously, say between 90C to 110C is not viewed as a paradox. Furthermore, the presumed continuous change in the extent of indistinguishability of the particles is now recognized as, in principle, invalid. Particles are either distinguishable or indistinguishable-there are no intermediate values of indistinguishability." Flying Jazz (talk) 20:59, 22 November 2007 (UTC)
Ignoring the first paragraph, I agree with everything written above by User:Flying Jazz. In addition, I also object to the statement by Lin:

Unfortunately it is well-known that none of the typical mixing processes have a detectable amount of heat and work transferred, even though a large amount of heat, up to the value calculated as TΔS (where T is temperature and S is thermodynamic entropy), should have been measured and a large amount of work up to the amount calculated as ΔG (where G is the Gibbs free energy) should have been observed.[9]

Lin completely ignores the fact that the entropy of mixing is offset by a change in the chemical potential(s) of the gas(es) yielding no change in the total energy. There is no PV work that "should have been observed". The reference [9] is not a reference at all but a "do not try this at home" warning. Lin has published papers on this subject in what seems to be respectable journals (e.g. Wiley interscience) which is why I hesitate to declare this stuff OR. It seems to me that these papers should be read before dumping these edits, which I have not yet done. Im really puzzled as to how this stuff got into a peer reviewed journal.
Articles by Lin:
PAR (talk) 23:11, 22 November 2007 (UTC)
My first paragraph above may have been too strong. Ben-Naim applies information theory to thermodynamics, so I shouldn't paint the entire discipline with such a broad brush. I agree with what PAR wrote. Simply mixing two ideal gases does not involve heat transfer and does not involve mechanical work. Alberty's IUPAC paper calls this type of work "chemical:no reactions" in table 1 of section 1.3, so it could be described as work being entirely spent on an entropy increase if system boundaries are drawn internal to the apparatus. I think if the barrier were replaced with a semi-permeable membrane, it would act like a piston, so PV work could be obtained from the same starting conditions. Obtaining useful work from isothermal isobaric concentration differences of distinguishable but very similar molecules is a huge part of how living systems generate useful work. See Template:Membrane transport. It probably takes a larger more complicated enzyme in most cases to distinguish between two similar molecules than it does to distinguish between two dissimilar molecules, so I could imagine charts with "similarity" on the x-axis and something on the y-axis like "enzyme kilodaltons", but it wouldn't be "entropy of mixing." I agree with PAR that this is not original research in Wikipedia because it has been published elsewhere, but I would call this a very NPOV article as it's currently written and possibly fringe because it lends undue weight to ideas that relate to other fields but would not be publishable in those fields. The best solution in my view would be to lend more relative weight in the article to people like Ben-Naim (hopefully there are many others like him) who make strong and sound criticisms of the concept and what Lin has done with it. Flying Jazz (talk) 18:01, 24 November 2007 (UTC)

WP:COI. Wikipedia editors must not use WP to advertise their own work, especially when it flies in the face of the general understanding of the topic.

Revert the lot. Jheald (talk) 17:10, 26 November 2007 (UTC)