Introduction to Modern Statistical Mechanics

Leading physical chemist David Chandler takes a new approach to statistical mechanics to provide the only introductory-level work on the modern topics of renormalization group theory, Monte Carlo simulations, time correlation functions, and liquid structure. The author provides compactsummaries of the fundamentals of this branch of physics and discussions of many of its traditional elementary applications, interspersed with over 150 exercises and microcomputer programs.

Thermodynamics, Fundamentals

3

(28)

First Law of Thermodynamics and Equilibrium

4

(4)

Second Law

8

(3)

Variational Statement of Second Law

11

(2)

Application: Thermal Equilibrium and Temperature

13

(3)

Auxiliary Functions and Legendre Transforms

16

(4)

Maxwell Relations

20

(2)

Extensive Functions and the Gibbs-Duhem Equation

22

(2)

Intensive Functions

24

(4)

Additional Exercises

25

(2)

Bibliography

27

(1)

Conditions for Equilibrium and Stability

28

(26)

Multiphase Equilibrium

29

(4)

Stability

33

(4)

Application to Phase Equilibria

37

(7)

Plane Interfaces

44

(10)

Additional Exercises

49

(3)

Bibliography

52

(2)

Statistical Mechanics

54

(32)

The Statistical Method and Ensembles

55

(4)

Microcanonical Ensemble and the Rational Foundation of Thermodynamics

59

(3)

Canonical Ensemble

62

(4)

A Simple Example

66

(3)

Generalized Ensembles and the Gibbs Entropy Formula

69

(3)

Fluctuations Involving Uncorrelated Particles

72

(2)

Alternative Development of Equilibrium Distribution Functions

74

(12)

Additional Exercises

79

(5)

Bibliography

84

(2)

Non-Interacting (Ideal) Systems

86

(33)

Occupation Numbers

89

(1)

Photon Gas

90

(2)

Phonon Gas or Fluctuations of Atomic Positions in a Cold Solid

92

(2)

Ideal Gases of Real Particles

94

(3)

Electrons in Metals

97

(3)

Classical Ideal Gases, the Classical Limit

100

(3)

Thermodynamics of an Ideal Gas of Structureless Classical Particles

103

(2)

A Dilute Gas of Atoms

105

(1)

Dilute Gas of Diatomic Molecules

106

(5)

Chemical Equilibria in Gases

111

(8)

Additional Exercises

113

(5)

Bibliography

118

(1)

Satistical Mechanical Theory of Phase Transitions

119

(40)

Ising Model

119

(5)

Lattice Gas

124

(1)

Broken Symmetry and Range of Correlations

125

(6)

Mean Field Theory

131

(4)

Variational Treatiment of Mean Field Theory

135

(4)

Renormalization Group (RG) Theory

139

(4)

RG Theory for the Two-Dimensional Ising Model

143

(6)

Isomorphism between Two-Level Quantum Mechanical System and the Ising Model

149

(10)

Additional Exercises

154

(4)

Bibliography

158

(1)

Monte Carlo Method in Satistical Mechanics

159

(29)

Trajectories

160

(3)

A Monte Carlo Trajectory

163

(5)

Non-Boltzmann Sampling

168

(7)

Quantum Monte Carlo

175

(13)

Additional Exercises

178

(4)

Bibliography

182

(2)

Appendix

184

(4)

Classical Fluids

188

(46)

Averages in Phase Space

189

(6)

Reduced Configurational Distribution Functions

195

(6)

Reversible Work Theorem

201

(1)

Thermodynamic Properties from g (r)

202

(5)

Measurement of g (r) by Diffraction

207

(2)

Solvation and Chemical Equilibrium in Liquids

209

(4)

Molecular Liquids

213

(5)

Monte Carlo for Hard Disks

218

(16)

Additional Exercises

223

(5)

Bibliography

228

(2)

Appendix

230

(4)

Statistical Mechanics of Non-Equilibrium Systems

234

(37)

Systems Close to Equilibrium

235

(2)

Onsager's Regression Hypothesis and Time Correlation Functions

237

(5)

Application: Chemical Kinetics

242

(4)

Another Application: Self-Diffusion

246

(6)

Fluctuation-Dissipation Theorem

252

(3)

Response Functions

255

(3)

Absorption

258

(3)

Friction and the Langevin Equation

261

(10)

Additional Exercises

266

(4)

Bibliography

270

(1)

Index

271

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Introduction to Modern Statistical Mechanics

Summary

Table of Contents

Supplemental Materials