Introduction to Statistical Physics, Second Edition

by Huang; Kerson

• ISBN13: 9781420079029
• ISBN10: 1420079026
• Edition: 2nd
• Format: Hardcover
• Copyright: 2009-09-21
• Publisher: Chapman & Hall/

Summary

Moving from basic to more advanced topics, this popular core text has been revised and expanded to reflect recent advances. While giving readers the tools needed to understand and work with random processes, it places greater focus on thermodynamics, especially the kinetics of phase transitions. The chapter on Bose'Einstein condensation has been revised to reflect improvements in the field. The edition also covers stochastic processes in greater depth, with a more detailed treatment of the Langevin equation. It provides new exercises and a complete solutions manual for qualifying instructors.

Table of Contents

Preface	p. xiii
A Macroscopic View of Matter	p. 1
Viewing the World at Different Scales	p. 1
Thermodynamics	p. 2
The Thermodynamic Limit	p. 3
Thermodynamic Transformations	p. 4
Classic Ideal Gas	p. 7
First Law of Thermodynamics	p. 8
Magnetic Systems	p. 9
Problems	p. 11
References	p. 13
Heat and Entropy	p. 15
The Heat Equations	p. 15
Applications to Ideal Gas	p. 16
Carnot Cycle	p. 19
Second Law of Thermodynamics	p. 20
Absolute Temperature	p. 21
Temperature as Integrating Factor	p. 22
Entropy	p. 25
Entropy of Ideal Gas	p. 26
The Limits of Thermodynamics	p. 27
Problems	p. 27
Using Thermodynamics	p. 33
The Energy Equation	p. 33
Some Measurable Coefficients	p. 34
Entropy and Loss	p. 35
TS Diagram	p. 37
Condition for Equilibrium	p. 39
Helmholtz Free Energy	p. 40
Gibbs Potential	p. 41
Maxwell Relations	p. 42
Chemical Potential	p. 42
Problems	p. 43
Phase Transitions	p. 47
First-Order Phase Transition	p. 47
Condition for Phase Coexistence	p. 49
Clapeyron Equation	p. 50
Van der Waals Equation of State	p. 51
Virial Expansion	p. 53
Critical Point	p. 53
Maxwell Construction	p. 55
Scaling	p. 56
Nucleation and Spinodal Decomposition	p. 57
Problems	p. 60
References	p. 63
The Statistical Approach	p. 65
The Atomic View	p. 65
Random Walk	p. 67
Phase Space	p. 69
Distribution Function	p. 70
Ergodic Hypothesis	p. 72
Statistical Ensemble	p. 72
Microcanonical Ensemble	p. 73
Correct Boltzmann Counting	p. 74
Distribution Entropy: Boltzmann's H	p. 76
The Most Probable Distribution	p. 77
Information Theory: Shannon Entropy	p. 78
Problems	p. 80
References	p. 82
Maxwell-Boltzmann Distribution	p. 83
Determining the Parameters	p. 83
Pressure of Ideal Gas	p. 84
Equipartition of Energy	p. 85
Distribution of Speed	p. 87
Entropy	p. 88
Derivation of Thermodynamics	p. 89
Fluctuations	p. 90
The Boltzmann Factor	p. 91
Time's Arrow	p. 92
Problems	p. 93
References	p. 97
Transport Phenomena	p. 99
Collisionless and Hydrodynamic Regimes	p. 99
Maxwell's Demon	p. 101
Nonviscous Hydrodynamics	p. 101
Sound Wave	p. 103
Diffusion	p. 103
Heat Conduction	p. 105
Viscosity	p. 106
Navier-Stokes Equation	p. 107
Problems	p. 109
References	p. 110
Canonical Ensemble	p. 111
Review of the Microcanonical Ensemble	p. 111
Classical Canonical Ensemble	p. 111
The Partition Function	p. 114
Connection with Thermodynamics	p. 114
Energy Fluctuations	p. 115
Minimization of Free Energy	p. 116
Classical Ideal Gas	p. 118
Problems	p. 119
Grand Canonical Ensemble	p. 123
The Particle Reservoir	p. 123
Grand Partition Function	p. 123
Number Fluctuations	p. 124
Connection with Thermodynamics	p. 125
Parametric Equation of State and Virial Expansion	p. 126
Critical Fluctuations	p. 127
Pair Creation	p. 128
Problems	p. 130
Noise	p. 133
Thermal Fluctuations	p. 133
Nyquist Noise	p. 134
Brownian Motion	p. 136
Einstein's Theory	p. 138
Diffusion	p. 140
Einstein's Relation	p. 142
Molecular Reality	p. 143
Fluctuation and Dissipation	p. 144
Brownian Motion of the Stock Market	p. 145
Problems	p. 148
References	p. 149
Stochastic Processes	p. 151
Randomness and Probability	p. 151
Binomial Distribution	p. 152
Poisson Distribution	p. 154
Gaussian Distribution	p. 155
Central Limit Theorem	p. 157
Shot Noise	p. 157
Problems	p. 160
References	p. 162
Time-Series Analysis	p. 163
Ensemble of Paths	p. 163
Ensemble Average	p. 164
Power Spectrum and Correlation Function	p. 165
Signal and Noise	p. 168
Transition Probabilities	p. 170
Markov Process	p. 171
Fokker-Planck Equation	p. 172
The Monte Carlo Method	p. 173
Simulation of the Ising Model	p. 176
Problems	p. 179
References	p. 181
The Langevin Equation	p. 183
The Equation and Solution	p. 183
Energy Balance	p. 185
Fluctuation-Dissipation Theorem	p. 187
Diffusion Coefficient and Einstein's Relation	p. 187
Transition Probability: Fokker-Planck Equation	p. 188
Heating by Stirring: Forced Oscillator in Medium	p. 189
Problems	p. 192
Quantum Statistics	p. 195
Thermal Wavelength	p. 195
Identical Particles	p. 197
Occupation Numbers	p. 198
Spin	p. 200
Microcanonical Ensemble	p. 201
Fermi Statistics	p. 202
Bose Statistics	p. 203
Determining the Parameters	p. 204
Pressure	p. 205
Entropy	p. 206
Free Energy	p. 207
Equation of State	p. 207
Classical Limit	p. 208
Problems	p. 210
Reference	p. 212
Quantum Ensembles	p. 213
Incoherent Superposition of States	p. 213
Density Matrix	p. 214
Canonical Ensemble (Quantum-Mechanical)	p. 216
Grand Canonical Ensemble (Quantum-Mechanical)	p. 217
Occupation Number Fluctuations	p. 219
Photon Bunching	p. 220
Problems	p. 221
References	p. 223
The Fermi Gas	p. 225
Fermi Energy	p. 225
Ground State	p. 226
Fermi Temperature	p. 227
Low-Temperature Properties	p. 228
Particles and Holes	p. 230
Electrons in Solids	p. 231
Semiconductors	p. 233
Problems	p. 235
The Bose Gas	p. 237
Photons	p. 237
Bose Enhancement	p. 239
Phonons	p. 241
Debye Specific Heat	p. 243
Electronic Specific Heat	p. 244
Conservation of Particle Number	p. 245
Problems	p. 246
References	p. 249
Bose-Einstein Condensation	p. 251
Macroscopic Occupation	p. 251
The Condensate	p. 253
Equation of State	p. 254
Specific Heat	p. 256
How a Phase is Formed	p. 257
Liquid Helium	p. 259
Problems	p. 260
References	p. 263
The Order Parameter	p. 265
The Essence of Phase Transitions	p. 265
Ginsburg-Landau Theory	p. 266
Relation to Microscopic Theory	p. 267
Functional integration and Differentiation	p. 268
Second-Order Phase Transition	p. 270
Mean-Field Theory	p. 271
Critical Exponents	p. 273
The Correlation Length	p. 274
First-Order Phase Transition	p. 277
Cahn-Hilliard Equation	p. 278
Problems	p. 278
References	p. 280
Superfluidity	p. 281
Condensate Wave Function	p. 281
Spontaneous Symmetry Breaking	p. 282
Mean-Field Theory	p. 284
Observation of Bose-Einstein Condensation	p. 285
Quantum Phase Coherence	p. 286
Superfluid Flow	p. 287
Phonons: Goldstone Mode	p. 289
Problems	p. 290
References	p. 292
Superconductivity	p. 293
Meissner Effect	p. 293
Magnetic Flux Quantum	p. 294
Josephson Junction	p. 296
DC Josephson Effect	p. 298
AC Josephson Effect	p. 299
Time-Dependent Vector Potential	p. 300
The SQUID	p. 300
Broken Symmetry	p. 302
Problems	p. 303
References	p. 303
Appendix	p. 305
Index	p. 313
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