Talk:Entropy (statistical thermodynamics)

message: 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)
thread_title:  Discrete quantum states? 

message: 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)
replies: text: 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)
thread_title:  Might want to discuss difference between Gibbs and Boltzmann for negative absolute temperature 

message: 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)
thread_title:  Suggest merge into [[Entropy]].  This article refers to the same "entropy" but different methods. 

message: 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)
replies: text: 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)
thread_title:  Why is E_i introduced? 

message: The first section states , but later down it states that the number of possible microstates is a natural number. Stowgull (talk) 00:39, 2 July 2023 (UTC)
thread_title:  Possible contradiction