Introduction to Modern Statistical Mechanics

Preface......Page 5
Contents......Page 9
A Note to the Students......Page 12
CHAPTER 1: Thermodynamics, Fundamentals......Page 15
1.1 First Law of Thermodynamics and Equilibrium......Page 16
1.2 Second Law......Page 20
1.3 Variational Statement of Second Law......Page 23
1.4 Application: Thermal Equilibrium and Temperature......Page 25
1.5 Auxiliary Functions and Legendre Transforms......Page 28
1.6 Maxwell Relations......Page 32
1.7 Extensive Functions and the Gibbs-Duhem Equation......Page 34
1.8 Intensive Functions......Page 36
Additional Exercises......Page 37
Bibliography......Page 39
CHAPTER 2: Conditions for Equilibrium  and Stability......Page 40
2.1 Multiphase Equilibrium......Page 41
2.2 Stability......Page 45
2.3 Application to Phase Equilibria......Page 49
2.4 Plane Interfaces......Page 56
Additional Exercises......Page 61
Bibliography......Page 64
CHAPTER 3: Statistical Mechanics......Page 66
3.1 The Statistical Method and Ensembles......Page 67
3.2 Microcanonical Ensemble and the Rational Foundation of 
Thermodynamics......Page 71
3.3 Canonical Ensemble......Page 74
3.4 A Simple Example......Page 78
3.5 Generalized Ensembles and the Gibbs Entropy Formula......Page 81
3.6 Fluctuations Involving Uncorrelated Particles......Page 84
3.7 Alternative Development of Equilibrium Distribution 
Functions......Page 86
Additional Exercises......Page 91
Bibliography......Page 96
CHAPTER 4: Non-Interacting (Ideal) Systems......Page 98
4.1 Occupation Numbers......Page 101
4.2 Photon Gas......Page 102
4.3 Phonon Gas or Fluctuations of Atomic Positions in a Cold
 Solid......Page 104
4.4 Ideal Gases of Real Particles......Page 106
4.5 Electrons in Metals......Page 109
4.6 Classical Ideal Gases, the Classical Limit......Page 112
4.7 Thermodynamics of an Ideal Gas of Structureless Classical
 Particles......Page 115
4.8 A Dilute Gas of Atoms......Page 117
4.9 Dilute Gas of Diatomic Molecules......Page 118
4.10 Chemical Equilibria in Gases......Page 123
Additional Exercises......Page 125
Bibliography......Page 130
5.1 Ising Model......Page 131
5.2 Lattice Gas......Page 136
5.3 Broken Symmetry and Range of Correlations......Page 137
5.4 Mean Field Theory......Page 143
5.5 Variational Treatment of Mean Field Theory......Page 147
5.6 Renormalization Group (RG) Theory......Page 151
5.7 RG Theory for the Two-Dimensional Ising Model......Page 155
5.8 Isomorphism between Two-Level Quantum Mechanical
 System and the Ising Model......Page 161
Additional Exercises......Page 166
Bibliography......Page 170
CHAPTER 6: Monte Carlo Method in Statistical Mechanics......Page 171
6.1 Trajectories......Page 172
6.2 A Monte Carlo Trajectory......Page 175
6.3 Non-Boltzmann Sampling......Page 180
6.4 Quantum Monte Carlo......Page 187
Additional Exercises......Page 190
Appendix......Page 196
CHAPTER 7: Classical Fluids......Page 200
7.1 Averages in Phase Space......Page 201
7.2 Reduced Configurational Distribution Functions......Page 207
7.3 Reversible Work Theorem......Page 213
7.4 Thermodynamic Properties from g(r)......Page 214
7.5 Measurement of g(r) by Diffraction......Page 219
7.6 Solvation and Chemical Equilibrium in Liquids......Page 221
7.7 Molecular Liquids......Page 225
7.8 Monte Carlo for Hard Disks......Page 230
Additional Exercises......Page 235
Bibliography......Page 240
Appendix......Page 242
CHAPTER 8: Statistical Mechanics of Non-Equilibrium Systems......Page 246
8.1 Systems Close to Equilibrium......Page 247
8.2 Onsager's Regression Hypothesis and Time Correlation Functions......Page 249
8.3 Application: Chemical Kinetics......Page 254
8.4 Another Application: Self-Diffusion......Page 258
8.5 Fluctuation-Dissipation Theorem......Page 264
8.6 Response Functions......Page 267
8.7 Absorption......Page 270
8.8 Friction and the Langevin Equation......Page 273
Additional Exercises......Page 278
Bibliography......Page 282
Index......Page 283