Equivalence of Canonical and Microcanonical Ensembles in Thermodynamic Limit

[nonequilibrium]

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?

 

[Jolb]

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.

 

[nonequilibrium]

Thank you, I will check it out. Can you give a page number?