Adiabatic sound waves 60
Andrade's viscosity model 118 122
Appell's cart 23
Barrier jumping via Lagrange's mechanics 13
Bill ashurst 92
Bird's approximation 75
Boltzmann equation 72
Boltzmann equation for diffusion 103 104 111
Boltzmann equation for heat flow 128
Boltzmann equation for viscosity 119
Bouncing ball and Lyapunov instability 8 9
Canonical probability density 17 29
Cantor set 107
Coexisting phases 69
Comoving frame 47
Compressible flow of phase-space probability 29
Conductivity for fluids 129
Conductivity for three hard disks 100 130
Constant-temperature (Gaussian) mechanics 26
Constant-temperature (Nose) mechanics 19
Constraint forces 92
Continuity equation of continuum mechanics 48
Continuum mechanics for shockwaves 82
Control theory 94
Corresponding states for heat conductivity 127
Corresponding states for viscosity 121
Crack healing 88
Crack inertia 88
Damped oscillators 28
Diatomic constraint force 24
Differential control 94 99
Diffusion coefficient for two hard disks 104
Diffusion equation solution from fourier series 125
Dislocation energy 89
Dislocations in solid plasticity 122
Displacement coordinates for elasticity calculations 57
Driving forces 92
Einstein conductivity model of Horrocks and McLaughlin 126
Einstein viscosity model of andrade 118
Elastic constants 59
Elastic strains 57
Elasticity 114
Energy equation of continuum mechanics 52
Enskog's viscosity model 118
Entropic variables 43
Equation of motion of continuum mechanics 50
Ergodicity 4 45
Eulerian coordinates 47
Evans — Gillan heat-current driving force 98 129
Eyring's viscosity model 122
Feedback 94
Fermi — Pasta — Ulam one-dimensional chain 35
Fick's first and second laws of diffusion 108
First law of thermodynamics 52
Force law for rare gases 72
Fourier heat conduction and thermal diffusivity 124
Fractals 106
Fragmentation simulation 84
Free volume and chemical potential 45
Friction coefficient  31 45
Future developments 132
Galton board 102
Gauss' mechanics 22
Gauss' principle 22 24
Gauss' principle failure for heat flow 129
Generalized (phase-space) continuity equation 27
Gibbs' variational principle 69
Grady — Glenn model for fragmentation 83
Gravitational forces and the thermodynamic limit 11
Gravity 1
Green — Kubo linear-response theory 98 101
Hamilton's mechanics 16
harmonic oscillator 19
Heat conducting chain 97
Heat conductivity for three hard disks 100 130
Heat flux vector 52
Heat theorem 54 59
Heat-current driving force 99
Heisenberg picture 47
Holonomic constraints 13
Homogeneous deformation 57
Hugoniot 80
Information theory 44
Information theory pitfall 105
Integral control 96 99
Interface between fluid and solid 92
Irreversibility 73 110
Irreversible thermodynamics of heat flow 125
Isokinetic canonical distribution 29
Isothermal constraint forces 94
Isothermal molecular dynamics 94
Jaynes — Zubarev distribution functions 101
Jaynes' information theory 44 105
Kepler's laws 1
Kolmogorov — Arnold — Moser tori 35
Lagrange multiplier 25
Lagrange's mechanics 13
| Lagrangian (comoving) coordinates 47
Lame elastic constants 115
Langevin equation 95
Lattice-coordinates virial theorem 56
Least action integral 14
Limit cycles (Rayleigh and van der Pol equations) 96
Liouville equation 31
Loschmidt objection 4
Lyapunov instability 6
Mayers' expansion of dense gas partition function 62
Mean-squared-displacement divergence in two dimensions 63
Mechanical variables 43
Melting of hard hyperspheres 65
Melting of two hard disks 65 66
Mesoscopic dynamics of dislocation motion 124
Mixing in phase space from periodic boundaries 34
Newton's mechanics 1
Newtonian molecular dynamics 72
Nonholonomic constraints 22
Nonlinear diffusion coefficient from molecular dynamics 113
Nonlinear nonholonomic constraints 23
Nonlinear response theory 101
Nose hamiltonian 20
Nose ideal gas 32
Nose mechanics derivations 31
Nose oscillator 20
Nose's mechanics 16 27
Number-dependence 62
One-dimensional chain 66
Periodic boundary conditions 10 63
Phase diagram for hard spheres 68
Phase-space mixing 34
Phonon scattering theory of heat conductivity 127
Phonons in a three-particle chain 98
Plane Couette flow 115
Plasticity 114
Poincare section for nose oscillator 35
Power loss 99
Pressure tensor 50 58
Pressure tensor symmetry 51
Principle of least constraint 22
Probability density in n-body system 27
Proportional control 95 99
Puncture plot 35
Radiation damage simulations 39
Rankine — Hugoniot equation 80
Rayleigh line for shockwave states 80
Rayleigh's equation for nonlinear oscillations 95
Relaxation-time Boltzmann equation 74 111 119 128
Reversibility 4
Reversibility paradox 35 73
Reynolds number 117
Rigid diatomic molecule using Gauss' principle 24
Rigor mortis school of continuum mechanics 115
Rigor mortis school of statistical mechanics 6
Rigorous kinetic theory 128
Rosenfeld relation for viscosity 121
Schroedinger picture 47
Second law of thermodynamics 4 37
Shear deformation 85
Shear thinning for two hard disks 106
Shockwave kurtosis 82
Shockwave profile 78
Shockwave simulation 77
Shockwave width 81
Sierpinski sponge 107
Stable motion 7
state variables 42
Steady-state atmosphere from Boltzmann's equation 111
Strain-rate tensor 114 115
Stress concentration 87
Symmetry of pressure tensor 51
Temperature 27 43
Temperature of a many-body system 26
Temperature-dependent hamiltonian of Nose 19
Thermodynamic limit 12 117
Three-particle harmonic chain 67 97
Time reversal 5 19
Time scaling of nose 21
Time-dependent perturbation theory 60
Toda potential for ideal gas energy 32
Triangular-lattice frequency distribution 86
Triatomic molecule with two holonomic constraints 14
Triple point simulation 69
Two-particle relaxation-time boltzmann equation 74
Uncertainty principle 9
Unstable motion 8 9
van der Pol's equation from Rayleigh's equation 95
Verlet (stoermer) algorithm 3
Virial theorem 2 54
Viscoelasticity 61
viscosity 114 121 122
Viscosity for two disks 65
Viscous hysteresis 116
Vortex shedding 75
Vorticity tensor 115
Zermelo — Poincare objection 4
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