Chapter 3. Rules of Calculation

  1. Prof. Dr. Debashish Chowdhury1 and
  2. Prof. Dr. Dietrich Stauffer2

Published Online: 28 JAN 2005

DOI: 10.1002/3527603158.ch3

Principles of Equilibrium Statistical Mechanics

Principles of Equilibrium Statistical Mechanics

How to Cite

Chowdhury, D. and Stauffer, D. (2000) Rules of Calculation, in Principles of Equilibrium Statistical Mechanics, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, FRG. doi: 10.1002/3527603158.ch3

Author Information

  1. 1

    Indian Institute of Technology, Kanpur, India

  2. 2

    University of Cologne, Germany

Publication History

  1. Published Online: 28 JAN 2005
  2. Published Print: 27 JUL 2000

ISBN Information

Print ISBN: 9783527403004

Online ISBN: 9783527603152

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Keywords:

  • statistical mechanics;
  • rules of calculation;
  • isolated classical systems;
  • closed classical systems;
  • open classical systems;
  • unified presentation of the rules;
  • maximum entropy principle;
  • illustration with ideal quantum gases;
  • quantum systems;
  • density operator

Summary

This chapter contains sections titled:

  • Introduction

  • Isolated Classical Systems

    • Boltzmann Hypothesis

    • Illustration with Ideal Classical Ising Magnet

    • Illustration with Ideal Classical Monatomic Gas

    • Entropy of Mixing and Gibbs' Paradox

    • Equipartition of Energy

    • Concepts of Ensemble and Ergodicity

  • Closed Classical Systems

    • The Partition Function

    • Connection with Thermostatics

    • Illustration with Ideal Classical Ising Magnet

    • Illustration with Ideal Classical Monatomic Gas

    • Equipartition of Energy

  • Open Classical Systems

    • Grand Partition Function

    • Connection with Thermostatics

    • Illustration with Ideal Classical Monatomic Gas

  • Unified Presentation of the Rules

    • Micro-canonical Ensemble

    • Canonical Ensemble

    • Grand-canonical Ensemble

  • Maximum Entropy Principle

    • Microcanonical Ensemble

    • Canonical Ensemble

    • Grand Canonical Ensemble

  • Illustration with Ideal Quantum Gases

    • Micro-Canonical Ensemble

    • Canonical Ensemble

    • Grand-Canonical Ensemble

  • Quantum Systems; Density Operator

    • Micro-Canonical Ensemble

    • Canonical Ensemble

  • Chapter Summary

  • Historical Notes

    • James Clerk Maxwell

    • Ludwig Boltzmann

    • Josiah Willard Gibbs

    • Maximum Entropy Principle

  • Problems

  • Supplementary Notes

    • Entropy Calculation from Trajectory

    • Entropy and Information

    • Wigner Function