Index 701Transfer matrix, 624–630
Transformation
bead-spring model, 150
block spin, 634–636, 638, 647
Carnot cycle, 59
Cartesian to dihedral angle, 354–355
center-of-mass, relative coordinates, 16
coordinate, 12
decimation, 647
gauge, 531
generalized coordinates, 12, 336, 337, 348
imaginary time, 407, 451
Legendre, 16–18
linearized renormalization group, 643
normal mode, 27, 480–481
pair cell, 648
parity, 617
Poincar ́e, 183
renormalization group, 636, 639
rotation matrix, 46
scaled coordinates, 165, 233, 237
second law of thermodynamics, 61
spatial warping, 363
spherical polar coordinates, 14
staging, 478
thermodynamic, 56, 76, 319, 338
time translation on phase space, 24, 65,
186, 332
translation group, 22
Transition frequency, 542
Transition path ensemble, 308
Transition path sampling, 305–312, 596–598
Transition rate, 542
Translation group, 22
Triple point, 610
Trotter factorization, 114, 117, 122, 132, 198,
205, 249, 254, 350, 493, 521
Trotter theorem, 110, 351, 451, 667–669
Umbrella potential, 343
Umbrella sampling, 343–347
Universality class, 178, 611
van der Waals theory
critical exponents, 179
equation of state, 175–177
Helmholtz free energy, 175
Partition function, 175
Vector potential, 392, 531
Velocity Verlet algorithm, 100–101, 113–115,
198, 298, 521, 595
Verlet algorithm, 99–100
Verlet list, 659
skin length, 659
update condition, 660
Vibrational dephasing, 588–591
Virial, 166
atomic, 247
coefficients, 168
energy estimator, 486, 488
equation of state, 168
heat-capacity estimator, 492
molecular, 248
pressure estimator, 489
second virial coefficient, 168, 420, 434, 443
Virial theorem
classical, 81–84, 96, 99, 146, 196, 205, 214,
507
path integral, 486
pressure, 226–227
tensorial, 232
work, 227–228
Volterra equation, 606Wang–Landau algorithm, 304–305, 347–348,
652
Wave equation, 532
Wave function, 377
WHAM, 344–347
Wick rotation, 451, 561
Wiener process, 592
Wiener–Khintchine theorem, 607
Work
free energy inequality, 319, 338
Jarzynski’s equality, 325–333, 362
mechanical, 2, 10, 21
thermodynamic, 57–61, 71, 72, 76–77, 221,
227, 232
virial theorem, 227, 232, 237, 239, 262
Work distribution, 331Zero-point energy, 404, 427