Talk:Entropy (statistical thermodynamics)

Discrete quantum states?

This article states: "Usually, the quantum states are discrete...." Is this true? If so, what is the explanation? (How is position discrete?) I would be interested to see some references. (I could not find the word "discrete" in the article on "quantum states"). 140.180.163.6 (talk) 05:47, 20 April 2008 (UTC)

Might want to discuss difference between Gibbs and Boltzmann for negative absolute temperature

As in, Gibbs works, Boltzmann doesn't work: http://web.mit.edu/newsoffice/2013/its-a-negative-on-negative-absolute-temperatures-1220.html?goback=%2Egde_36972_member_5822015646686277636#%21 — Preceding unsigned comment added by 66.14.154.3 (talk) 23:17, 28 December 2013 (UTC)

The odd thing about that article is they focus only on results applying to the the microcanonical ensemble, and though they say they read Gibbs it seems they didn't notice his warnings against both the "Boltzmann entropy" and "Gibbs entropy" (as they are called in the article). Both have problems, though the Boltzmann entropy certainly has more problems. Besides these, Gibbs also discussed a third definition of entropy in the context of the canonical ensemble, and in that case the negative absolute temperatures are again permitted, for some special kinds of systems (the system's density of states must vanish sufficiently quickly at high energies). The correspondence of this third entropy to the thermodynamic entropy is very appealing, even outside the thermodynamic limit. You can find Gibbs' thoughts in Elementary Principles in Statistical Mechanics, especially in chapter XIV. I recently added text to the microcanonical ensemble article on just this topic, so have a read. --Nanite (talk) 21:10, 2 January 2014 (UTC)

Suggest merge into Entropy. This article refers to the same "entropy" but different methods.

I've added a template at top of article suggesting moving into Entropy, just as Entropy (classical thermodynamics) has a similar proposal to merge into Entropy. It isn't a different "entropy" that's the subject of this article; just a different theory or model or set of methods for analyzing/understanding/explaining entropy or making predictions about phenomena. DavRosen (talk) 16:10, 22 July 2013 (UTC)

Why is E_i introduced?

In section "Gibb's Entropy Formula," the article states:

For a classical system (i.e., a collection of classical particles) with a discrete set of microstates, if $E_{i}$ is the energy of microstate i, and $p_{i}$ is the probability that it occurs during the system's fluctuations, then the entropy of the system is

$S=-k_{\text{B}}\,\sum _{i}p_{i}\ln \,p_{i}$

Why is the variable $E_{i}$ introduced? It isn't used anywhere in the article.

Is the sentence trying to say that the sum is taken over all possible energies of the system, and $p_{i}$ is the probability that the system is in a microstate with energy $i$? That doesn't seem right. Norbornene (talk) 15:07, 10 September 2017 (UTC)

Good for you to point that out -- indeed for the most general definition of entropy, the energy E_i doesn't matter. What matters is just summing over all microstates. Note though that it's important to distinguish "summing over all energies" from "summing over all states" because these two sums are only the same when every state has a distinct energy. --Nanite (talk) 16:53, 10 September 2017 (UTC)

I also came here to ask why $E_{i}$ is there. I think it has to do with the derivation in the right-hand box titled "Entropy changes for systems in a canonical state", which says $ln(p_{i})=E_{i}/k_{B}T-ln(Z)$. But this 'Z' isn't mentioned anywhere else! -- Philgoetz (talk) 01:44, 24 August 2024 (UTC)

The part connected to Gibbs entropy is incorrect

1. Classical systems normally do not have a discreet set of microstates - the allowed classical microstates occupy some space in 6N phase-space of the whole system (hence the probability to observe a given microstate is zero and the proposed formula gives an infinity). N is the number of particles.

2. The Gibbs formula can be applied only to systems in thermodynamic equilibrium - deep down it is based on Liouville theorem (which proves that all classical states reachable during the dynamics can be described by the same probability density) and ergodic assumption. It can not be applied to driven systems out of equilibrium where the Liouville theorem does not apply.

3. Gibbs definition of equilibrium, however, is different from Boltzmann one - it is based on temporal ensemble. Hence it can be applied to a single system (say, Universe) and can show fluctuations. Still does not explain the fluctutation law for which one needs mixing condition.

4. Shannon and Neumann lived after Gibbs - so they copied Gibbs not the other way round.

5. I support merging this article with entropy one which at the moment is skewed too much in favour of old classical thermodynamics and neglects great progress made by science later (end of XIX-XX centuries).

Article issues and classification

Article may have been accidentally assessed at B-class. The B-class assessment states, The article is suitably referenced, with inline citations. It has reliable sources, and any important or controversial material which is likely to be challenged is cited.

Not only is the article tagged with "relies excessively on references to primary sources" it has inline "citation needed" tags. There is far too much unsourced content, especially with equations. Reassess article to C-class.

Possible contradiction

The first section states The large number of particles of the gas provides an infinite number of possible microstates for the sample, but later down it states that the number of possible microstates is a natural number. Stowgull (talk) 00:39, 2 July 2023 (UTC)