Contents -- Preface -- Preface to the First Edition -- Glossary of Technical Terms -- 1. Time Reversibility, Computer Simulation, Algorithms, Chaos -- 1.1 Microscopic Reversibility -- Macroscopic Irreversibility -- 1.2 Time Reversibility of Irreversible Processes -- 1.3 Classical Microscopic and Macroscopic Simulation -- 1.4 Continuity, Information, and Bit Reversibility -- 1.5 Instability and Chaos -- 1.6 Simple Explanations of Complex Phenomena -- 1.7 The Paradox: Irreversibility from Reversible Dynamics -- 1.8 Algorithm: Fourth-Order Runge-Kutta Integrator -- 1.9 Example Problems -- 1.9.1 Equilibrium Baker Map -- 1.9.2 Equilibrium Galton Board -- 1.9.3 Equilibrium Hookean Pendulum -- 1.9.4 Nose-Hoover Oscillator with a Temperature Gradient -- 1.10 Summary and Notes -- 1.10.1 Notes and References -- 2. Time-Reversibility in Physics and Computation -- 2.1 Introduction -- 2.2 Time Reversibility -- 2.3 Levesque and Verlet's Bit-Reversible Algorithm -- 2.4 Lagrangian and Hamiltonian Mechanics -- 2.5 Liouville's Incompressible Theorem -- 2.6 What Is Macroscopic Thermodynamics? -- 2.7 First and Second Laws of Thermodynamics -- 2.8 Temperature, Zeroth Law, Reservoirs, Thermostats -- 2.9 Irreversibility from Stochastic Irreversible Equations -- 2.10 Irreversibility from Time-Reversible Equations? -- 2.11 An Algorithm Implementing Bit-Reversible Dynamics -- 2.12 Example Problems -- 2.12.1 Time-Reversible Dissipative Map -- 2.12.2 A Smooth-Potential Galton Board -- 2.13 Summary -- 2.13.1 Notes and References -- 3. Gibbs' Statistical Mechanics -- 3.1 Scope and History -- 3.2 Formal Structure of Gibbs' Statistical Mechanics -- 3.3 Initial Conditions, Boundary Conditions, Ergodicity -- 3.4 From Hamiltonian Dynamics to Gibbs' Probability -- 3.5 From Gibbs' Probability to Thermodynamics -- 3.6 Pressure and Energy from Gibbs' Canonical Ensemble.

3.7 Gibbs' Entropy versus Boltzmann's Entropy -- 3.8 Number-Dependence and Thermodynamic Fluctuations -- 3.9 Green and Kubo's Linear-Response Theory -- 3.10 An Algorithm for Local Smooth-Particle Averages -- 3.11 Example Problems -- 3.11.1 Quasiharmonic Thermodynamics -- 3.11.2 Hard-Disk and Hard-Sphere Thermodynamics -- 3.11.3 Time-Reversible Confined Free Expansion -- 3.12 Summary -- 3.12.1 Notes and References -- 4. Irreversibility in Real Life -- 4.1 Introduction -- 4.2 Phenomenology - the Linear Dissipative Laws -- 4.3 Microscopic Basis of the Irreversible Linear Laws -- 4.4 Solving the Linear Macroscopic Equations -- 4.5 Nonequilibrium Entropy Changes -- 4.6 Fluctuations and Nonequilibrium States -- 4.7 Deviations from the Phenomenological Linear Laws -- 4.8 Causes of Irreversibility a la Boltzmann and Lyapunov -- 4.9 Rayleigh-Benard Algorithm with Atomistic Flow -- 4.10 Rayleigh-Benard Algorithm for a Continuum -- 4.11 Three Rayleigh-Benard Example Problems -- 4.11.1 Rayleigh-Benard Flow via Lorenz' Attractor -- 4.11.2 Rayleigh-Benard Flow with Continuum Mechanics -- 4.11.3 Rayleigh-Benard Flow with Molecular Dynamics -- 4.12 Summary -- 4.12.1 Notes and References -- 5. Microscopic Computer Simulation -- 5.1 Introduction -- 5.2 Integrating the Motion Equations -- 5.3 Interpretation of Results -- 5.4 Control of a Falling Particle -- 5.5 Second Law of Thermodynamics -- 5.6 Simulating Shear Flow and Heat Flow -- 5.7 Shockwaves -- 5.8 Algorithm for Periodic Shear Flow with Doll's Tensor -- 5.9 Example Problems -- 5.9.1 Isokinetic Nonequilibrium Galton Board -- 5.9.2 Heat-Conducting One-Dimensional Oscillator -- 5.9.3 Many-Body Heat Flow -- 5.10 Summary -- 5.10.1 Notes and References -- 6. Shockwaves Revisited -- 6.1 Introduction -- 6.2 Equation of State Information from Shockwaves -- 6.3 Shockwave Conditions for Molecular Dynamics.

6.4 Shockwave Stability -- 6.5 Thermodynamic Variables -- 6.6 Shockwave Profiles from Continuum Mechanics -- 6.6.1 Shockwave Profile with Shear Viscosity -- 6.6.2 Shockwave Profile with Viscosity and Conductivity -- 6.6.3 Shockwave Profiles with Tensor Temperatures -- 6.6.4 Flow Algorithm with Maxwell-Cattaneo Time Delays -- 6.7 Comparing Model Profiles with Molecular Dynamics -- 6.8 Lyapunov Instability in Strong Shockwaves -- 6.9 Summary -- 6.9.1 Notes and References -- 7. Macroscopic Computer Simulation -- 7.1 Introduction -- 7.2 Continuity and Coordinate Systems -- 7.3 Macroscopic Flow Variables -- 7.4 Finite-Difference Methods -- 7.5 Finite-Element Methods -- 7.6 Smooth Particle Applied Mechanics [SPAM] -- 7.7 A SPAM Algorithm for Rayleigh-Benard Convection -- 7.7.1 Initial Conditions -- 7.7.2 SPAM Evaluation of the Particle Densities -- 7.7.3 SPAM Evaluation of { u } and { T } -- 7.7.4 SPAM Evaluation of the Constitutive Relations -- 7.8 Applications of SPAM to Rayleigh-Benard Flows -- 7.8.1 SPAM with and without a Core Potential -- 7.8.2 SPAM and Kinetic-Energy Fluctuations -- 7.9 Summary -- 7.9.1 Notes and References -- 8. Chaos, Lyapunov Instability, Fractals -- 8.1 Introduction -- 8.2 Continuum Mathematics -- 8.3 Chaos -- 8.4 The Spectrum of Lyapunov Exponents -- 8.5 Fractal Dimensions -- 8.6 A Simple Ergodic Fractal -- 8.7 Fractal Attractor-Repeller Pairs -- 8.8 A Global Second Law from Reversible Chaos -- 8.9 Coarse-Grained and Fine-Grained Entropy -- 8.10 Oscillators, Lyapunov Algorithms, Fractal Dimensions -- 8.10.1 A Thought-Provoking Oscillator Exercise -- 8.10.2 Doubly-Thermostated Oscillator -- Lyapunov Spectra -- 8.10.3 Lyapunov Spectra for a Chaotic Double Pendulum -- 8.10.4 Coarse-Grained Galton Board Entropy -- 8.10.5 Color Conductivity -- 8.11 Summary -- 8.11.1 Notes and References -- 9. Resolving the Reversibility Paradox.

9.1 Introduction -- 9.2 Irreversibility from Boltzmann's Kinetic Theory -- 9.3 Boltzmann's Equation Today -- 9.4 Gibbs' Statistical Mechanics -- 9.5 Jaynes' Information Theory -- 9.6 Green and Kubo's Linear Response Theory -- 9.7 Thermomechanics -- 9.8 The Delay Times Separating Causes from their Effects -- 9.9 A Fluctuation Theorem -- 9.10 Are Initial Conditions Relevant? -- 9.11 Constrained Hamiltonian Ensembles -- 9.12 Anosov Systems and Sinai-Ruelle-Bowen Measures -- 9.13 Trajectories versus Distribution Functions -- 9.14 Are Maps Relevant? -- 9.15 Irreversibility Time-Reversible Motion Equations -- 9.16 Boltzmann-Equation Shockwave-Structure Algorithm -- 9.17 Summary -- 9.17.1 Notes and References -- 10. Afterword-a Research Perspective -- 10.1 Introduction -- 10.2 What do We Know? -- 10.3 Why Reversibility is Still a Problem -- 10.4 Change and Innovation -- 10.5 Role of Examples -- 10.6 Role of Chaos and Fractals -- 10.7 Role of Mathematics -- 10.8 Remaining Puzzles -- 10.9 Summary -- 10.10 Acknowledgments -- Bibliography -- Index.