Index
Action integral, 29–32, 463
imaginary time, 465
harmonic oscillator, 469
Action-angle variables, 94
Adiabatic free energy dynamics, 348–355
Affine connection, 13
After-effect function, 553
Amplitude
classical wave, 366, 532
probability, 366
Angular momentum, 14
Angular velocity, 40
Anticommutator, 547
Areal velocity, 15
Autocorrelation function
classical, 504
harmonic oscillator, 512
Mori–Zwanzig theory, 602
pressure tensor, 508
rigid-bond approximation, 603
velocity, 510, 583, 588
vibrational dephasing, 587–591
dipole and infrared spectrum, 550–551
quantum, 546
harmonic oscillator, 548–550
velocity, 561
Baker–Campbell–Hausdorff formula, 123
Banach space, 667
Blue moon ensemble, 336–342
Body-fixed frame, 39
Boiling curve, 610
Boltzmann statistics, 413
Boltzmann’s constant, 71, 77
Boltzmann’s relation, 77, 222
Bose–Einstein condensation, 409, 432, 440
Bose–Einstein distribution function, 438
Boundary conditions
determination of energy levels, 382
Lees–Edwards, 518
periodic, 126, 207, 382, 392, 410, 624, 626,
630, 652, 656, 661
Box matrix, 229
Box–Muller sampling, 102–104
Bra vector, Dirac, 368
Bromwich contour, 672
Brownian particle, 583–584
Bulk viscosity, 528
CardinalB-spline function, 664
Carnot cycle, 59–60
Cell matrix, 229
Central limit theorem, 281–285
Central potential, 14
Chemical potential, 57, 76, 136, 137, 212,
219, 220, 226, 265, 267, 296, 421,
422, 431, 433
Clausius inequality, 61
Coexistence curves, 610
Committor distribution, 359–361
histogram test, 360
Commutator, 109, 373
Conservation law
action, 94
Andersen’s equations, 239
areal velocity, 15
blue moon ensemble, 340
conservation of energy, 11
energy, 7
Martyna–Tobias–Klein equations, 245
Nos ́e–Hoover chain equations, 193
Nos ́e–Hoover equations, 190
GSLLOD dynamics, 525
Hamiltonian, 20, 78
isokinetic equations, 204
Jarzynski’s equality, 329
linear momentum, 22
Martyna–Tobias–Klein equations, 245
Nos ́e–Hoover equations, 191
Martyna–Tobias–Klein equations, 242
Noether’s theorem, 22
non-Hamiltonian equilibrium phase space
distribution, 189
non-Hamiltonian phase space volume, 187
orbital angular momentum, 14
phase space distribution, 69
phase space volume, 66
planar Couette flow, 506
Poisson bracket, 22
shadow Hamiltonian, 122
Constant-energy hypersurface, 21, 78
Constant-energy surface, 21
Constraint
Gauss’s principle, 36
holonomic, 32, 104–108, 202, 256
nonholonomic, 32
Contraction semigroup, 667
Control variables
canonical ensemble, 135
grand canonical ensemble, 267, 268