Talk:Gibbs paradox

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1 Category - Quantum mechanics
2 Suggestions
3 Dimensions
4 No paradox, and no need to introduce indistinguishability of particles
5 Disputed
6 too technical tag

[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] Suggestions

"This article or section be merged with Mixing paradox"? Because they are very similar this merging should be very acceptable. However, "Mixing paradox" article should be deleted and "Gibbs Paradox" stays.--Linshukun 23:20, 25 February 2007 (UTC)

Contents should be added because there are different resolutions. Gibbs himself or Jaynes provided only one of several resolutions. I would like to help to prepare a good paper "Gibbs Paradox". In the moment I prepared "An Introduction", in a great hurry. I did not touch any other existing paragraphs. A table of contents is the following:

1. Introduction.

Significance, background, definition....

2. Classical Thermodynamic Resolution.

Better called consideration or explanation, in stead of resolution.

3. Statistical Mecahnics Resoltion

4. Quantum Mechanics Resoltion

5. Information Theorey Resolution.

(Shu-Kun Lin will volunteer this section)

6. Concluding Remarks

References

Links

Interested guys please contact me (Shu-Kun Lin) by e-mail lin@mdpi.org, subject title "Gibbs Paradox".--Linshukun 23:20, 25 February 2007 (UTC)

[edit] Dimensions

The number of states $φ / h 3$ , 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 lenght^3N×momentum^3N-1 and not lenght^3N×momentum^3N . 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)

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