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An Introduction to Statistical Mechanics and Thermodynamics$
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Robert H. Swendsen

Print publication date: 2012

Print ISBN-13: 9780199646944

Published to Oxford Scholarship Online: December 2013

DOI: 10.1093/acprof:oso/9780199646944.001.0001

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Ensembles in Classical Statistical Mechanics

Ensembles in Classical Statistical Mechanics

Chapter:
(p.201) 19 Ensembles in Classical Statistical Mechanics
Source:
An Introduction to Statistical Mechanics and Thermodynamics
Author(s):

Robert H. Swendsen

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199646944.003.0019

This chapter resumes the discussion of classical statistical mechanics that was begun in Part 1 of the book. Numerical methods (molecular dynamics and Monte Carlo computer simulations) of calculating thermodynamic properties from statistical mechanics are defined and investigated in the problems at the end of the chapter. The Liouville theorem is proved, and its consequences discussed. It is shown how thermodynamic identities can be derived entirely from the formalism of statistical mechanics, as well as how new identities can be derived that go beyond those in thermodynamics. The properties of the harmonic oscillator are derived explicitly because of their importance in future chapters.

Keywords:   microcanonical ensemble, molecular dynamics, Monte Carlo computer simulations, Liouville theorem, thermodynamic identities, harmonic oscillator

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