Is there a general H-theorem?

+ 5 like - 0 dislike
147 views

In statistical mechanics, Boltzmann showed that for dilute gases the H-function increases. I remember from a lecture that there is no general H-theorem, e.g. for non-dilute gases or in the quantum case but there seem to be also claims to the contrary. So what is the status of the (generalised) H-theorem?

This post imported from StackExchange Physics at 2016-08-02 12:32 (UTC), posted by SE-user corto

edited Aug 2, 2016
Boltzmann has shown his $H$ function decreases in time (under certain assumptions).

This post imported from StackExchange Physics at 2016-08-02 12:32 (UTC), posted by SE-user Ján Lalinský
@JánLalinský - I thought Boltzmann defined a priori the $H$-function to decrease because it corresponded to the physical "direction" of time?

This post imported from StackExchange Physics at 2016-08-02 12:32 (UTC), posted by SE-user honeste_vivere
@honeste_vivere, no, why do you think that? $H$ function is defined as functional of probability distribution. It decreases in some situations and increases in other.

This post imported from StackExchange Physics at 2016-08-02 12:32 (UTC), posted by SE-user Ján Lalinský
@JánLalinský - I recall reading it in one of Cedric Villani's books and several others. Boltzmann was criticized by some other big name for doing this and his response was for them to propose a situation where $H$ would change in the opposite sense. I forget now but I definitely recall reading something along these lines.

This post imported from StackExchange Physics at 2016-08-02 12:32 (UTC), posted by SE-user honeste_vivere

 Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead. To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL. Please consult the FAQ for as to how to format your post. This is the answer box; if you want to write a comment instead, please use the 'add comment' button. Live preview (may slow down editor)   Preview Your name to display (optional): Email me at this address if my answer is selected or commented on: Privacy: Your email address will only be used for sending these notifications. Anti-spam verification: If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:p$\hbar$ysi$\varnothing$sOverflowThen drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds). To avoid this verification in future, please log in or register.