Does the Equal A Priori Probabilities Assumption Hold for Interacting Gases?

[gonadas91]

Hi! My question has to be with the equal a priori probabilities assumption in the microcanonical ensemble when we consider an interacting system, that is, particles interacting between them but no external work or heat is done over the system. Does this assumption still hold for such a system? Thanks!

 

[Chandra Prayaga]

Yes. If the system is in equilibrium, all microstates are equally probable, even for an interacting system.

 

[gonadas91]

So, because the interactions don't depend on time, the hamiltonian must be a conserved quantity according to Noether's theorem, and the total energy is conserved or fixed. However, I would like to know more about how to define equilibrium for a system of many interacting particles. Is there any reference to look at this closer? Also, the ergodic assumption is of interest for me, in the case of an interacting system. If you assume the equal a priori probabilities, then for very long times, all states are visited regularly with the same frecuency. Is there any reference too to see how this works? Or any attempts to prove that that have been made?

Thank you!

 

[Chandra Prayaga]

Several references on ergodicity in interacting systems. I just typed those words in google and got may pages.