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| Chandler D. — Introduction to modern statistical mechanics |
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| Ïðåäìåòíûé óêàçàòåëü |
Absorption 258—261
action 176
Adiabatic 5
Adiabatic, thermodynamic processes 6 8
Adiabatic, walls 5
Associated and nonassociated liquids 215 218
Born — Oppenheimer approximation 106—109 152 188 189
Bose condensation 95
Bosons 89 90 94—96
Boyle temperature 206
Broken symmetry 125—131 153 158 178 181
Brownian motion 264—265
Capillary waves 183 see
Causality 256
Cavity distribution function 213 227
Chemical equilibria 111—12 113 211—213
Chemical kinetics 242—246 267—269
Chemical potential in chemical equilibria 111
Chemical potential in phase equilibria 37—52
Chemical potential of a classical ideal gas 74 112 117
Chemical potential, excess and solvation 211 213 225 226
Chemical potential, thermodynamic definition 16—17
Chemical potential, weighting particle number fluctuations 70—74 86 95—100
Clausius — Clapeyron equation 39—40 52
Coexistence lines and regions 38—44
Compressibility, definition 35 36
Compressibility, governing density functions 83
Compressibility, stability criteria 35 36 71
Configuration space and distribution 190 192—229
Conformational equilibria and transitions 84 113 209 213 215
Conservation of energy in first law 5
Conservation of particles in diffusion 247
Continuity, equation of 247 248
Convexity 29 71 see "Stability"
Coordination shells 198 214 215 217 218
Correlation functions 127 178—179 see "Time
Correlation length or range of 59 127—129 178
Coupling parameter method 210
Critical exponents 123 135 147
Critical fluctuations and opalescence 84 129—131
Critical point 38 39 44 45 83 130—131 see
Critical temperature 121—149 166
Curie temperature 121 166
de Broglie wavelength 115 194
Debye solid 94
Density fluctuations 72 73 83 84
Detailed balance 165 242
Diffraction see "X-ray scattering"
Diffusion 246—252 267 269
Dirac delta function 80 244—245 247 256
Dissipation 261 see "Response
Einstein solid 94
Energy of many phases 29—34
Energy of surfaces 29 45—49
Energy, conservation 5
Energy, fluctuations 65—66
Energy, internal 4
Energy, kinetic 190—193 203
Energy, minimum principle 12
Energy, potential 203—204
Ensemble, Canonical 62—66
Ensemble, definition 57
Ensemble, equivalency 65
Ensemble, generalized 69—71
Ensemble, Grand Canonical 70—71
Ensemble, microcanonical 59—62
Enthalpy 19
Entropy for ideal gases 106 117
Entropy, statistical definition 61
Entropy, thermodynamic definition 9—16
Equilibrium between phases 37
Equilibrium, criteria 28—53
Equilibrium, states 6 7
Ergodic 58 161 239—240 see
Exponential relaxation 252 265
Extensive properties 4 22—24
Fermi energy 98
Fermi function 97—100
Fermi momentum 98
fermions 89 90 96—100 114—116
Fick’s law 248
Fields, thermodynamic 33
First law of thermodynamics 4—8
First-order transition 39 40
Fixed points 142—143 147
Fluctuation-dissipation theorem see also "Absorption" "Langevin
Fluctuation-dissipation theorem, application to chemical relaxation 243 244
Fluctuation-dissipation theorem, application to diffusion 249—251
Fluctuation-dissipation theorem, derivation 252—254
Fluctuation-dissipation theorem, statement 241 254—255
Flux 245 247 248
Fractals 158
Friction 261 see
Functional 176 255 256
Gibbs entropy formula 70 71 74—79
Gibbs free energy 19
Gibbs — Bogoliubov — Feynman bound 138 228
Gibbs — Duhem equation 22—24
Green — Kubo formulas 251
Hard disk fluid, equation of state 227
Hard disk fluid, Monte Carlo of 218—223
Hard rod fluid 224 225
harmonic oscillator 90 93 109 223 260 261—262 265—266
Heat 5
Heat capacity of Ising model 123 147—148
Heat capacity of low temperature metal 100
Heat capacity of water 218
Heat capacity, definition 16
Heat capacity, governing energy fluctuations 66
Heat capacity, stability criteria 34 71
Helmholtz free energy, excess (relative to ideal gas) 205 206 211
Helmholtz free energy, from the canonical partition function 64
Helmholtz free energy, thermodynamic definition 19
Henry’s law 225
Henry’s Law, constant 211 226
homogeneous functions 22—24 26
Hydrogen bonding 215—218
Hydrophobic effect 53
ICE 218
Ideal gas 72—74 86—118
Importance sampling 163
Inertial motion 250
Inexact differential 6
Infrequent event 171 see
Integral equation theories 220
Intensive properties 10
INTERFACE see "Surface"
Internal constraint 11—13 28—53
Internal energy see "Energy" "First
Intramolecular distribution 213 214
Irreversible 9 see
Ising model 120—158
Ising model of phase transitions 120—149
Ising model, isomorphic to quantum tunneling system 149—153
Ising model, Monte Carlo trajectory 164—185
Kadanoff transformation 140 144
Langevin equation, and the second fluctuation-dissipation theorem 264
Langevin equation, derivation 261—263
Langevin equation, for vibrational spectra 265—266
Langevin equation, generalized 264
Langevin equation, without memory 264
Lattice gas 124—125 130—131
Legendre transforms 16—20 62 69
Lennard — Jones potential 202—203
Linear response 234—236 see "Response
Linear response of harmonic systems 262
Liquid 41—45 see
Liquid structure of molecular fluids 213—218
Liquid structure of simple fluids 197—201
| localization see "Self-trapping" "Two-state
Long ranged order 120 125—131
Magnetization of independent spins 80—81
Magnetization, fluctuations 81 128—129 174
Magnetization, Markovian approximation 264
Magnetization, spontaneous 120—137 171—175 182
Magnetization, thermodynamic work 50
Mass action, law of 112
Master equation 165
Maxwell construction 41—44
Maxwell relations 20—22
Maxwell — Boltzmann distribution see "Velocity or momentum distribution"
Mean field theory 131—138 219 220
Metals 97—100
Mixed valence compound 81—83 see
Molecular dynamics simulation 159
Monte Carlo 159—187 219—223
Monte Carlo, Metropolis algorithm 165 176 220 221
Monte Carlo, non-Boltzmann sampling 168—175
Monte Carlo, quantum path integral 175—178
Monte Carlo, smart or force-bias 180
Natural process see "Irreversible"
Neutron scattering 207
Non-equilibrium, ensemble average 236 237 242 253
Non-equilibrium, statistical mechanics of 234—270
Normal modes 92
Occupation numbers 89—103
Order parameter 127
Order-disorder transition 121 see
Pair correlation function 197 224 see
Pair potential 202—203
Partial molar 24
Partition function for solvation 209
Partition function in classical limit 100—104 189—191
Partition function of harmonic lattice 92—94
Partition function of ideal gases 86—117
Partition function of Ising magnet 121—123 135—149
Partition function of lattice gas 124—125
Partition function, canonical 64
Partition function, grand canonical 71
Partition function, rotational 109—110
Partition function, translational 105
Partition function, two-level quantum system 149—151 157
Partition function, vibrational 110
Pass, in Monte Carlo 173 174
Path integrals and sums 151 189 see quantum
Pauli exclusion principle 90 203 see
phase diagram 38—44
Phase rule 38
Phase space 56 189—192 236 240 242 252 254
Phase transitions see also "Equilibrium between
Phase transitions, statistical mechanics of 119—158
Phonons 89 92
Photon gas 90—91
Planck distribution 91
Potential of mean force 202 see
Quantum effects in fluids 189 194 195 see "Fermions"
Quasi-ergodic 162—163 169 170
Radial distribution function 197
Radial distribution function for gas 198—199 205
Radial distribution function for hard disks 221—223 226—227
Radial distribution function for molecular liquids 213—218
Radial distribution function for simple fluid 198—209
Radial distribution function for simple solid 199—200
Radial distribution function for solvation 210—211 226
Radial distribution function in perturbation theory 228
Random number generator 164—165 179
Rare event 169—170
Rate constant 242—246 268 269
Reduced configurational distribution, functions 195—229
Reduced configurational distribution, generic 196
Reduced configurational distribution, specific 196
Regression hypothesis 237 239 241 243 248 see
Relaxation 58 236—270 see "Regression "Time
Renormalization group (RG) 139—149 155
Response functions 255—258
Reversible 8
Reversible work function for atoms in liquids 201—202
Reversible work function for fluids at low density 205
Reversible work function for magnetization of the Ising model 126 158 171—175
Reversible work function for solvation and chemical equilibrium 209—213 225—226
Second law of thermodynamics 8—13
Second law of thermodynamics, implications to equilibria and stability 28—53
Second law of thermodynamics, statistical meaning 61
Second law of thermodynamics, variational statement of 11—13
Second-order phase transition 39 40
Self-consistent mean field 133
Self-diffusion constant 248—252 267—269
Self-similarity 158
Self-trapping 153 181—182
Semiconductor 116
Simulation 54 159 219 see
Solids, conduction electrons 97—100 116
Solids, harmonic approximation 92—94
Solids, radial distributions 199—200
Solvation energy 83 210 see
Spinodal 44
Stability, thermodynamic criteria 13—15 33—37 41 44 49—53 71
State(s) see also "Occupation numbers" "Phase
State(s), density of 60
State(s), equilibrium macroscopic 6 7
State(s), function 9
State(s), microscopic 55
State(s), stationary quantum 56 58
Stationary system see "Time correlation functions"
Statistical uncertainty in simulations 162
Stirling’s approximation 67
Stochastic molecular dynamics 265
Stokes’ law 267
Structure factor 208
Surface, energetics 44—49 122 125—131 174
Surface, fluctuations 49 131 179 183
Surface, Gibbs dividing 47—48
Surface, tension 45 126
susceptibility 50 81 128 see
Symmetry number 109
Temperature see also "Ensemble canonical"
Temperature, thermal equilibrium 13—16
Temperature, thermodynamic definition 10
Thermal wavelength 112 115 116 193—194
Thermodynamic perturbation theory 135—38 169 227—228
Time correlation functions 238—70
Time correlation functions and absorption 260
Time correlation functions and response functions 257
Time correlation functions for chemical populations 243—246
Time correlation functions for orientations 240—241
Time correlation functions for velocities 240—241 251—252 265 266 269
Time correlation functions, stationarity property for equilibrium systems 239 251
Trajectory 56—57 160—163 221—222 239—240 245 246
Transition state theory 245—246
Triple point 38 44
Two-state quantum system, broken symmetry of 153 158 178 181
Two-state quantum system, canonical ensemble of 82—83
Two-state quantum system, isomorphism with Ising magnet 149—154 157
Two-state quantum system, Monte Carlo of 175—178 180—182 185—187
Umbrella sampling 169—175
Van der Waals equation 43 52 83
Van der Waals picture 229
Velocity or momentum distribution 192—194
Virial coefficient 206
Virial theorem 205 226—227
viscosity 267 268 269
Water, density maximum 25 218
Water, equilibrium with ice 40—42
Water, heat capacity 218
Water, hydrogen bonds 216
Water, liquid structure 216—218
Water, quantum effects 195
Work 5
X-ray scattering 207—209
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