Index 695adiabatic dynamics, 348–355
blue moon ensemble, 342
blue moon ensemble, 337
collective variables, 334
conjugate momenta, 19
Hamiltonian, 19
harmonic bath model, 572–575
Lagrangian, 13
Liouville’s theorem, 64
phase space compressibility, 23
reaction coordinates, 334
Generalized Langevin equation
derivation from harmonic bath, 575–578
derivation from Mori–Zwanzig theory,
598–604
dynamic caging, 582
friction kernel, 580–582
potential of mean force, 578
random force, 578–580
Gibbs free energy, 220, 225, 267
magnetic mean-field, 620–621
one-dimensional Ising model, 626
two-dimensional Ising model, 628
Gibbs paradox, 92–93
Graph theory
two-dimensional Ising model, 630–633
Green–Kubo relation
bulk viscosity, 528
diffusion constant, 510
shear viscosity, 508
Hamilton’s equations, 20
driven oscillator, 496
energy conservation, 20
formal solution, 109
incompressibility, 23
Jarzynski equality, 327
linear response theory, 497
Liouville’s theorem, 64
microcanonical ensemble, 98
Newton’s second law, 20
symplectic structure, 23
time reversibility, 101
Hamiltonian
action-angle variables, 94
adiabatic dynamics, 348, 357
Andersen, 238
canonical distribution, 139
conservation of, 20
constant-energy surface, 21
constant-pressure molecular dynamics, 234
definition, 19
eigenvalue equation, 374
electromagnetic field, 532
free particle, 87, 144, 380
generalized coordinates, 19
Hamilton’s equations, 20
harmonic bath, 575, 578
harmonic bead-spring model, 147
harmonic oscillator, 93, 146, 383, 512
ideal gas, 88, 145, 409
interaction picture, 535
Ising model
block spin transformation, 636
general, 614
mean-field, 619
one-dimensional, 624
two-dimensional, 626
zero-field, 617
isoenthalpic-isobaric distribution, 221
Lagrangian, 19
λ-dynamics, 322
Liouville equation, 70
Liouville operator, 108
microcanonical distribution, 78
normal mode, 27
Nos ́e, 180
Nos ́e–Poincar ́e, 184
operator, 373
path-integral molecular dynamics
classical isomorphic, 477, 483
staging, 479
Poisson bracket, 22
quaternion, 119
raising and lowering operators, 385
shadow, 121–124
spin lattice, 613
temperature-accelerated molecular
dynamics, 357
thermal contact, 84
time-dependent perturbation, 533, 552
virial theorem, 81
Hard-sphere potential, 173
Heat capacity
classical harmonic oscillator, 147
constant pressure, 226
constant volume, 142, 279
critical point behavior, 178, 612, 615
definition, 57
discontinuity, 441, 445
energy fluctuations in canonical ensemble,
143
ideal gas, 146, 229
low-temperature ideal boson gas, 441
low-temperature ideal fermion gas, 431
mean-field theory, 623
molar, 142
quantum harmonic oscillator, 404
two-dimensional Ising model, 629
virial estimator, 492
Heaviside step function, 82, 131, 605
Heisenberg Hamiltonian, 613
Heisenberg uncertainty principle, 375
Helmholtz free energy, 136, 141, 231, 266
adiabatic free energy dynamics, 325, 349
difference as partition function ratio, 316
difference from blue moon ensemble,
337–339, 342
difference from Jarzynski’s equality, 326