694 Index
uniform ensemble, 83
Equala prioriprobability, 78
Equation of state
critical exponentδ, 178, 616
definition, 56
grand canonical ensemble, 268, 272–273
high-temperature ideal boson gas, 434
high-temperature ideal fermion gas, 420
ideal gas, 56, 91, 146, 228, 274
Ising model, 614
isochores, 91
isotherms, 91
low-temperature ideal boson gas, 440
low-temperature ideal fermion gas, 432
mean-field Ising model, 622
simple fluid, 610
van der Waals, 175–177, 648
virial, 168
Ergodic hypothesis, 98
Ergodic system, 98
Error function, 657
Estimator
classical energy, 163
classical molecular pressure, 248
classical pressure, 166
classical pressure tensor, 233–237
energy, primitive path integral, 461, 475
energy, virial path integral, 486, 489
heat capacity, virial path integral, 492
Monte Carlo, 281
path integral, 459
pressure tensor, path integral, 492
pressure, primitive path integral, 462, 475
pressure, virial path integral, 489
Euler angles, 43
Euler’s theorem, 224, 265–267, 487
Euler–Lagrange equation, 10
action integral, 31
central potential, 14
Euclidean, 466
generalized coordinates, 12
harmonic oscillator, 11
path integral, 465
Ewald summation, 657, 660–666
smooth particle-mesh, 663–666
Excluded volume, 174–175
Expectation value, 366, 372
Fermi energy, 422
Fermi sign problem, 474
Fermi surface, 409, 423
Fermi’s Golden Rule, 544
Fermi–Dirac distribution, 422, 430
First law of thermodynamics, 57–58, 76, 327
Fluctuations
canonical energy, 142–144
isobaric volume, 262
Force
adiabatically averaged, 351
central potential, 14
conservative, 3
constraint, 37, 105, 256, 340
determination of hydrodynamic boundary
conditions, 526
external driving, 496–497
external driving, general, 498
external in nonequilibrium molecular
dynamics, 517–520
generalized, 338
Hooke’s law, 7, 125
linear driving, 508–509
long-range, 166, 660
multiple time-scale motion, 116
nonbonded, 656
pair-wise, 166
projection onto surface of constraint, 36
random, 578–580
shear, 495, 505–506
short-range
link list, 660
switching function, 658
truncation, 658
Verlet list, 659
simple force field, 115
torque, 42
van der Waals, 126
Force constant, Hooke’s law, 7
Free energy
Gibbs, 220
grand canonical, 267, 268
Helmholtz, 136
Free energy calculations
adiabatic free energy dynamics, 348–355
blue moon ensemble, 336–342
free energy perturbation, 315–318
Jarzynski’s equality, 325–333
λfree energy dynamics, 322–325
metadynamics, 355–359
thermodynamic integration, 318–321
umbrella sampling, 343–347
Wang–Landau algorithm, 347–348
Free energy perturbation, 315–318
Free energy profile, 322, 323, 336–342
quantum in malonaldehyde, 490
Friction kernel, 578, 580–582
exponential, 584–585
static friction coefficient, 581
Fugacity, 273, 417, 432, 433
Functional integral, 462–471
Functional integration
expansion about classical path, 468–471Galilean relativity, 39
Gas constant, 56
Gauge invariance, 531
Gauss’s equation of motion, 37
Gauss’s principle, 36
Gaussian random process, 580
Generalized coordinates, 12
action integral, 29