Preface......Page 3
Contents......Page 7
List of figures......Page 15
What is statistical mechanics?......Page 21
Quantum dice......Page 24
Probability distributions......Page 25
Waiting times......Page 26
Stirling and asymptotic series......Page 27
Random matrix theory......Page 28
Six degrees of separation......Page 29
Satisfactory map colorings......Page 32
Random walk examples: universality and scale invariance......Page 35
The diffusion equation......Page 39
Currents and external forces......Page 40
Solving the diffusion equation......Page 42
Green......Page 43
Random walks in grade space......Page 45
Molecular motors and random walks......Page 46
Perfume walk......Page 47
Fourier and Green......Page 48
Periodic diffusion......Page 49
Polymers and random walks......Page 50
Stocks, volatility, and diversification......Page 51
Computational finance: pricing derivatives......Page 52
Building a percolation network......Page 53
The microcanonical ensemble......Page 57
Configuration space......Page 59
Momentum space......Page 61
What is temperature?......Page 64
Pressure and chemical potential......Page 67
Advanced topic: pressure in mechanics and statistical mechanics.......Page 68
Entropy, the ideal gas, and phase-space refinements......Page 71
Exercises......Page 73
Pressure computation......Page 74
Connecting two macroscopic systems......Page 75
Microcanonical energy fluctuations......Page 76
Gauss and Poisson......Page 77
Solving differential equations: the pendulum......Page 78
Liouville's theorem......Page 83
Ergodicity......Page 85
Equilibration......Page 89
Invariant measures......Page 90
Jupiter! and the KAM theorem......Page 92
Entropy as irreversibility: engines and the heat death of the Universe......Page 97
Entropy as disorder......Page 101
Entropy of mixing: Maxwell's demon and osmotic pressure......Page 102
Residual entropy of glasses: the roads not taken......Page 103
Entropy as ignorance: information and memory......Page 105
Non-equilibrium entropy......Page 106
Information entropy......Page 107
Exercises......Page 110
Burning information and Maxwellian demons......Page 111
Black hole thermodynamics......Page 113
Pressure--volume diagram......Page 114
The Arnol'd cat map......Page 115
Chaos, Lyapunov, and entropy increase......Page 116
Entropy of glasses......Page 117
Rubber band......Page 118
How many shuffles?......Page 119
Shannon entropy......Page 120
Fractal dimensions......Page 121
Deriving entropy......Page 122
Free energies......Page 125
The canonical ensemble......Page 126
Uncoupled systems and canonical ensembles......Page 129
Grand canonical ensemble......Page 132
What is thermodynamics?......Page 133
Mechanics: friction and fluctuations......Page 137
Chemical equilibrium and reaction rates......Page 138
Free energy density for the ideal gas......Page 141
Exercises......Page 143
Exponential atmosphere......Page 144
Negative temperature......Page 145
Molecular motors and free energies......Page 146
Laplace......Page 147
Euler......Page 148
Barrier crossing......Page 149
Michaelis--Menten and Hill......Page 151
Pollen and hard squares......Page 152
Statistical mechanics and statistics......Page 153
Mixed states and density matrices......Page 155
Advanced topic: density matrices.......Page 156
Quantum harmonic oscillator......Page 159
Bose and Fermi statistics......Page 160
Non-interacting bosons and fermions......Page 161
Maxwell--Boltzmann `quantum' statistics......Page 164
Free particles in a box......Page 166
Black-body radiation......Page 167
Bose condensation......Page 168
Metals and the Fermi gas......Page 170
Ensembles and quantum statistics......Page 171
Phonons and photons are bosons......Page 172
Does entropy increase in quantum systems?......Page 173
Light emission and absorption......Page 174
Einstein's A and B......Page 175
Bosons are gregarious: superfluids and lasers......Page 176
Semiconductors......Page 177
Bose condensation: the experiment......Page 178
The photon-dominated Universe......Page 179
White dwarfs, neutron stars, and black holes......Page 181
The Ising model......Page 183
Magnetism......Page 184
Binary alloys......Page 185
How to solve the Ising model......Page 186
Markov chains......Page 187
What is a phase? Perturbation theory......Page 191
Ising fluctuations and susceptibilities......Page 194
Red and green bacteria......Page 195
Implementing Ising......Page 196
Implementing Wolff......Page 197
Stochastic cells......Page 198
The repressilator......Page 199
Hysteresis and avalanches......Page 202
Hysteresis algorithms......Page 205
NP-completeness and kSAT......Page 206
Order parameters, broken symmetry, and topology......Page 211
Define the order parameter......Page 212
Examine the elementary excitations......Page 216
Classify the topological defects......Page 218
Topological defects in nematic liquid crystals......Page 223
Topological defects in the XY model......Page 224
Defect energetics and total divergence terms......Page 225
Landau theory for the Ising model......Page 226
Symmetries and wave equations......Page 229
Superfluid order and vortices......Page 230
Superfluids: density matrices and ODLRO......Page 231
Correlation functions: motivation......Page 235
Experimental probes of correlations......Page 237
Equal-time correlations in the ideal gas......Page 238
Onsager's regression hypothesis and time correlations......Page 240
Susceptibility and linear response......Page 242
Dissipation and the imaginary part......Page 243
Static susceptibility......Page 244
The fluctuation-dissipation theorem......Page 247
Causality and Kramers--KrΓΆnig......Page 249
Microwave background radiation......Page 251
Pair distributions and molecular dynamics......Page 253
Damped oscillator......Page 255
Telegraph noise in nanojunctions......Page 256
Fluctuation-dissipation: Ising......Page 257
Magnetic dynamics......Page 258
Quasiparticle poles and Goldstone's theorem......Page 259
Stable and metastable phases......Page 261
Maxwell construction......Page 263
Nucleation: critical droplet theory......Page 264
Coarsening......Page 266
Dendritic growth......Page 270
Maxwell and van der Waals......Page 271
Interfaces and van der Waals......Page 272
Nucleation in the Ising model......Page 273
Nucleation of dislocation pairs......Page 274
Origami microstructure......Page 275
Minimizing sequences and microstructure......Page 278
Snowflakes and linear stability......Page 279
Continuous phase transitions......Page 283
Universality......Page 285
Scale invariance......Page 292
Examples of critical points......Page 297
Quantum criticality: zero-point fluctuations versus energy......Page 298
Dynamical systems and the onset of chaos......Page 299
Glassy systems: random but frozen......Page 300
Perspectives......Page 301
Scaling and coarsening......Page 302
Bifurcation theory......Page 303
The onset of lasing......Page 304
Renormalization-group trajectories......Page 305
Superconductivity and the renormalization group......Page 306
Period doubling......Page 308
The renormalization group and the central limit theorem: long......Page 311
Percolation and universality......Page 313
Hysteresis and avalanches: scaling......Page 316
Fourier conventions......Page 319
Derivatives, convolutions, and correlations......Page 322
Fourier methods and function space......Page 323
Fourier and translational symmetry......Page 325
Double sinusoid......Page 327
Fourier Gaussians......Page 328
Fourier relationships......Page 329
Aliasing and windowing......Page 330
Gibbs phenomenon......Page 331
References......Page 333
Index......Page 343
EndPapers......Page 370