Equivalence of Canonical and Microcanonical Ensembles in Thermodynamic Limit

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SUMMARY

The equivalence of canonical and microcanonical ensembles in the thermodynamic limit is established under specific conditions, primarily the existence of a thermodynamic limit. Mehran Kardar's textbook, "Statistical Physics of Particles," provides a comprehensive analysis of this equivalence, particularly in Lectures 12, 13, and 14. These lectures detail the conditions under which both ensembles yield the same predictions, making it a crucial resource for understanding this topic. The online version of the lecture notes is available at MIT's website.

PREREQUISITES
  • Understanding of thermodynamic limits in statistical mechanics
  • Familiarity with canonical and microcanonical ensembles
  • Knowledge of statistical physics principles
  • Ability to interpret graduate-level physics texts
NEXT STEPS
  • Study Mehran Kardar's "Statistical Physics of Particles" for detailed insights
  • Review Lectures 12, 13, and 14 from Kardar's online lecture notes
  • Explore additional resources on the conditions for ensemble equivalence
  • Investigate other statistical mechanics textbooks for comparative analysis
USEFUL FOR

Graduate students in physics, researchers in statistical mechanics, and educators seeking to deepen their understanding of ensemble theory and its applications in thermodynamics.

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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?
 
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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.
 


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

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