Equivalence of microcanonical & canonical ensemble: necessary/sufficient conditions

  • #1
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Main Question or Discussion Point

In a lot of practical situations it is simply assumed the canonical and microcanonical ensemble give the same predictions, and that's fine, but I'm interested in a more exact statement of when they are indeed equivalent (in the thermodynamic limit). First of all, a thermodynamic limit must exist. But I'm sure there most be other conditions on the system. Can anybody give some suggestions, arguments or references?
 

Answers and Replies

  • #2
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Mehran Kardar's textbook "Statistical Physics of Particles" has a very in-depth demonstration of how each of the ensembles leads to the same predictions. The entire book is basically contained in his "Lecture Notes" which are posted online.
http://web.mit.edu/8.333/www/lectures/index.html
You'll find the answer in Lectures 12, 13, and 14. Granted, this is a graduate-level text that most of my fellow graduates found unintelligible, but it does answer your question.
 
  • #3
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Thank you, I will check it out. Can you give a page number?
 

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