Index 697Local density approximation, 426–430
Loschmidt’s paradox, 55
M(RT)^2 algorithm, 289–297
Markov chain, 289
Martyna–Tobias–Klein equations
flexible cell, 244
isotropic, 242
Massive thermostatting, 197, 479
Maxwell construction, 619
tie line, 648
Maxwell’s equations in vacuum, 531
Maxwell–Boltzmann distribution, 101
Mean-field theory
Ising model, 619–623
van der Waals, 618–619
Mean-square displacement, 511
Melting curve, 610
Memory function, 602
Memory integral, 580
Memory kernel, 580, 602
Metadynamics, 355–359
Metric
mass metric tensor, 13
phase space metric, 186–188
Minimum image convention, 659
Modular invariance, 519, 523
Molecular dynamics, 75, 96–99
adiabatic free energy dynamics, 322–325,
348–355
centroid, 562–564
classical propagator, 108–115
constraints, 104–108
hybrid Monte Carlo, 297–300
initial conditions, 101–104
isoenthalpic-isobaric ensemble, 237–240
isokinetic algorithm, 202–207
isothermal-isobaric ensemble
flexible cell, 243–247
integrators, 249–254
isotropic, 240–243
ROLL algorithm, 256–261
Langevin, 591–595
liquid structure, 207–208
metadynamics, 355–359
microcanonical
alanine dipeptide, 128–130
harmonic oscillator, 125–126
Lennard–Jones fluid, 126–128
multiple time-scale integration, 115–118
nonequilibrium, 517–527
Nos ́e algorithm, 180–183
Nos ́e–Hoover algorithm, 185
Nos ́e–Hoover chain algorithm, 192–202
Nos ́e–Poincar ́e algorithm, 183–184
path integral, 476–483
replica exchange Monte Carlo, 301
ring-polymer, 564–565
shadow Hamiltonian, 121–124
symplectic quaternions, 119–121
time correlation functions, 512–517
velocity Verlet algorithm, 100–101
Verlet algorithm, 99–100
Wang–Landau algorithm, 305
Moment of inertia, 40, 44
Monte Carlo
acceptance ratio, 290
canonical ensemble, 292–295
central limit theorem, 281–285
detailed balance, 289
grand canonical ensemble, 296–297
hybrid, 297–300
importance sampling, 287–289
isothermal-isobaric ensemble, 295–296
M(RT)^2 algorithm, 289–297
particle insertion/deletion, 296
pass, 293, 485
path integral, 484–486
rejection methods, 290
replica exchange, 304
replica-exchange, 300
spin lattice, 652
Wang–Landau algorithm, 304–305,
347–348
Mori–Zwanzig theory, 598–604Newton, Isaac, 1
laws of motion, 1–4
second law
differential equation, 2, 4
free particle, 3
harmonic oscillator, 7
Noether’s theorem, 22
Non-Hamiltonian
classical statistical mechanics, 185–191
dynamical system, 37, 186
Nonholonomic constraint, 32
Nos ́e Hamiltonian, 180
Nos ́e–Hoover chain equations, 193
Nos ́e–Hoover equations, 185
Nos ́e–Poincar ́e Hamiltonian, 184Occupation number, 412
One-particle density matrix, 427
Onsager regression hypothesis, 504
Operator
anticommutator, 547
classical Liouville, 108–115, 498, 499, 599
classical propagator, 109
commutator, 109, 373
constant of the motion, 379
density matrix, 397–399
Heisenberg picture, 379
Hermitian, 369
idempotent, 599
incompatible observables, 373
Interaction picture, 535
projection, 598–599
quantum Liouville, 400
raising and lowering, 386, 606