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| Honerkamp J. — Statistical physics: an advanced approach with applications |
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| Предметный указатель |
Irreversible process 291
Ising model 122 123
Ising model, anisotropic 123
Ising model, one-dimensional 128
Ising model, two-dimensional 139
Isobaric expansion coefficient 79
Isobaric expansivity 79
Isochoric tension coefficient 80
Isothermal compressibility 78
Isothermal compressibility, critical exponent of 110
Isotherms, for a Bose gas 241
Isotherms, in a van der Waals gas 104
Isotropic Heisenberg model 281
Ito type, stochastic integral of 187
Jackknife method 451
Joule — Thomson coefficient 489
Joule — Thomson experiment 489
Kalman filter 421
Kalman filter, backward 422
Kalman filter, extended 423
Kalman filter, forward 421
Kalman gain 421
Kirchhoff's law 252
Kolmogorov system of axioms 6
Lack of information 25
Lame elastic constants 261
Landau free energy 146
Landau level 274
Landau theory of diamagnetism 272
Langevin equation 186
Large deviation property 48
Latent heat 107
Law of mass action 478
Laws of thermodynamics 298
Least-squares estimator 327 332 391 407
Least-squares FIR filter 352
Legendre transform 47
Levy process 204
Lifetime density function 324
Likelihood 322
Limit theorem, central 36
Linear congruence method 471
Liouville equation 163
Log likelihood function 322
Long-range dependence 204
Lorentz distribution 21
Low-pass filter 348
LS estimator see "Least-squares estimator"
Lyapunov function 305
Macrocanonical system 68
magnetic moment 125
Magnetic susceptibility, in mean field approximation 137
magnetization 125
Magnon 284
MAP see "Maximum a posteriori estimator"
Marginal density 13
Markov assumption 157
Markov field 118
Markov process 157
Markov process, piecewise deterministic 176
Markov process, temporally homogeneous 157
Markov property 157
Master equation 161
Maximum a posteriori estimator 387 405 407
Maximum entropy method 413
Maximum entropy principle 28 52
Maximum likelihood estimator 322 330 387
Maxwell construction 105
Maxwell relations 81
Maxwell — Boltzmann distribution 35
Mean squared error 311
Median 22
Metropolis algorithm 182
Metropolis sampler 182
Meyer filter 373
Microcanonical system 52
Minimum entropy production, principle of 305
Missing data 400
Mixed state 214
Model selection 405
Molecular dynamics calculation 97
Moment, mth 19
Monte Carlo integration 313
Monte Carlo method, for random fields 181
Morlets 373
Moving Average 348
Moving average filter 349
MSE see "Mean squared error"
Multilevel logistic model 123
Multiplicative noise 187
Multiresolution 377
n-vector models 144
Neighborhood 117
Neural network 463
Neutron star 234
Normal distribution 10
Normal distribution, covariance matrix 20
Normal distribution, higher moments 19
Nuisance parameter 389
Null hypothesis 445
Number of microstates 53
Nyquist frequency 343
Observation equation 403
Occupation number representation 169 221
Occupation number, average, for quasi-particles 279
Occupation number, average, of ideal Fermi gas 226
One-step process 166
Optical branch 262
Orbitals 220
Ornstein — Uhlenbeck process 188 203
Pade approximation 96
Paramagnetic substance 272
Paramagnetic system, ideal 127
Paramagnetism 277
Parametric model 328
Particle bath 68
Partition function 60 119
Partition function, grand canonical 68
Partition function, macrocanonical 68
Partition function, T-p system 66
Pattern 116
Pauli equation 164
Percus — Yevick equation 100
Periodogram 343
Phase of a filter 348
Phase transition 48
Phase transition, first order 107
Phonon 259
Photon 245
Planck's radiation law 247
Point estimation 310
Poisson distribution 12 22
Poisson process 167 175
Potts model 124
Power of a test 451
Pressure 63
probability 7
probability distribution 8
Probability, conditional 14
Probability, joint 14
Process without memory 157
Product of random variables 34
Pseudo-inverse 330
Pure state 214
Quantile 22
Quantile of standard normal distribution 23
Quasi-particles 233 278
Quasi-static process 292
Radial distribution function 85 170
| Radiation pressure 254
Radioactive decay 166 174
Random number 9
Random number generator 37 471
Random sample 310 327
Random variable 9
Random variable,  -distributed 35
Random variable,  -distributed 34 335
Random variable, Bernoulli distributed 10
Random variable, binomally distributed 10
Random variable, gamma distributed 49
Random variable, Gaussian distributed 10
Random variable, Poisson distributed 12 22
Random variable, t-distributed 35
Random variable, uniformly distributed 10
Random walk 166 173
Randomvector 12
Rayleigh — Jeans formula 248
Realization 6
Recursive filter 350
Red noise 159
Regularization method 414
Regularization parameter 414
Rejection method 482 497
Relative frequency interpretation 309
Relaxation-time spectrum 414
Relaxator 210
Response function 76 190
Reversible process 291 292
Riemann zeta function 237
Roton 286
Sample 310
Sample, independent 322
Sampling frequency 339
Sampling time 339
Scale, of a base function 379
Scaling function, in multiresolution 378
Scaling relations 111
Self-consistent method 409
Self-similar processes 203
Set of events, complete and disjoint 7 15 24
Short-time expansion 160
Significance level 445
Simulation, of a piecewise deterministic Markov process 177
Singular value 331
Singular value decomposition 330 335
Six-vertex model 144
Sixteen-vertex model 144
Smoothed pseudo-Wigner distribution 365
Smoothing filter 348
Solar constant 254
Space of events 6
Specific heat 76
Specific heat, critical exponent of 110
Specific heat, for ideal Bose gas 241
Spectrogram 363
Spectrum of a process 340
Spin wave 284
Spontaneous expansion 293
Spontaneous magnetization 284
Stable density 39
Standard deviation 19
Standard method 316
Standard method for Monte Carlo integration 314
Standard normal distribution 10
State space model 404
Static structure function 89
Stationary distribution 158
Stationary quantities, simulation 180
Statistical dependence 15
Statistical independence 20
Statistical system with dissipation 191
Stefan — Boltzmann constant 248
Stefan — Boltzmann law 253
Stochastic differential equation 185
Stochastic differential equation, numerical integration 189
Stochastic integral 186
Stochastic process 156
Stochastic process, Gaussian 188
Stochastic time step, algorithm with 178
Stop-band 348
Stratonovich type, stochastic integral of 187
Strictly stable density 39
Structure function, dynamical 90
Structure function, static 89
Student t-distribution 35
Sum rule for random variablevS 33
Superconductivity 287
Superfluid  243
Superfluidity 286
susceptibility 76 126 190
Sweep 183
Symlets 373
Taper 357
Temperature 56
Temporally homogeneous Markov process 157
Tensor product 331
Test quantity 445
Test statistic 445
Test, -Test 455
Test, F-Test 454
Test, F-Test for least-squares estimators 458
Test, Kolmogorov — Smirnov Test 457
Test, Likelihood-Ratio Test 459
Test, t-Test 452
Test, z-Test 452
Texture 117
Thermodynamic limit 48
Thermodynamic potential 222
Thermodynamic potential for molecules with inner degrees of freedom 266
Thermodynamic potential, ideal Bose gas 234
Thermodynamic potential, ideal Fermi gas 225
Thermodynamic potential, photon gas 248
Throw of a die 7
Time-frequency distribution 363
Transfer function 347
Transfer matrix 129
Transfer matrix for the two-dimensional Ising model 141
Transition probability 157
Tschebyshev filter 354
Two-time covariance 158
Unbiased estimator 311
Uncertainty relation 53
Uniform prior 391
valence electrons 231
Van Leeuwen, theorem of 272
Vapor pressure curve 107
Variance 19
Variance of normal distribution 19
Virial coefficients 92
Virial expansion 92
Virial theorem 87
Viterbi algorithm 417
Volume bath 65
Waiting time distribution 179
Wavelet 379
Weighted average 325
Weiss domain 285
White dwarfs 233
White noise 121 158 159
White random field 127
Widom relation 151
Wien's displacement law 248
Wien's radiation law 248
Wiener — Khinchin theorem 344
Wigner — Ville distribution 365
Wigner — Ville spectrum 364
Window function 351
Work 290
Zero point pressure 231
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