- Title Pages
- Dedication
- Preface
- Acknowledgments
- 1 Introduction
- 2 The Classical Ideal Gas
- 3 Discrete Probability Theory
- 4 The Classical Ideal Gas: configurational Entropy
- 5 Continuous Random Numbers
- 6 The Classical Ideal Gas:Energy-Dependence of Entropy
- 7 Classical Gases: Ideal and Otherwise
- 8 Temperature, Pressure, Chemical Potential, and All That
- 9 The Postulates and Laws of Thermodynamics
- 10 Perturbations of Thermodynamic State Functions
- 11 Thermodynamic Processes
- 12 Thermodynamic Potentials
- 13 The Consequences of Extensivity
- 14 Thermodynamic Identities
- 15 Extremum Principles
- 16 Stability Conditions
- 17 Phase Transitions
- 18 The Nernst Postulate: the Third Law of Thermodynamics
- 19 Ensembles in Classical Statistical Mechanics
- 20 Classical Ensembles: Grand and Otherwise
- 21 Irreversibility
- 22 Quantum Ensembles
- 23 Quantum Canonical Ensemble
- 24 Black-Body Radiation
- 25 The Harmonic Solid
- 26 Ideal Quantum Gases
- 27 Bose–Einstein Statistics
- 28 Fermi–Dirac Statistics
- 29 Insulators and Semiconductors
- 30 Phase Transitions and the Ising Model
- Appendix: Computer Calculations and VPython
- Index

# 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

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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- Title Pages
- Dedication
- Preface
- Acknowledgments
- 1 Introduction
- 2 The Classical Ideal Gas
- 3 Discrete Probability Theory
- 4 The Classical Ideal Gas: configurational Entropy
- 5 Continuous Random Numbers
- 6 The Classical Ideal Gas:Energy-Dependence of Entropy
- 7 Classical Gases: Ideal and Otherwise
- 8 Temperature, Pressure, Chemical Potential, and All That
- 9 The Postulates and Laws of Thermodynamics
- 10 Perturbations of Thermodynamic State Functions
- 11 Thermodynamic Processes
- 12 Thermodynamic Potentials
- 13 The Consequences of Extensivity
- 14 Thermodynamic Identities
- 15 Extremum Principles
- 16 Stability Conditions
- 17 Phase Transitions
- 18 The Nernst Postulate: the Third Law of Thermodynamics
- 19 Ensembles in Classical Statistical Mechanics
- 20 Classical Ensembles: Grand and Otherwise
- 21 Irreversibility
- 22 Quantum Ensembles
- 23 Quantum Canonical Ensemble
- 24 Black-Body Radiation
- 25 The Harmonic Solid
- 26 Ideal Quantum Gases
- 27 Bose–Einstein Statistics
- 28 Fermi–Dirac Statistics
- 29 Insulators and Semiconductors
- 30 Phase Transitions and the Ising Model
- Appendix: Computer Calculations and VPython
- Index