Non-Equilibrium Statistical Mechanics by Prigogine, Ilya -- Read -- Imperial Library of Trantor

Index

Cover Title page Copyright Page Contents Introduction 1. The Liouville Equation

1. The Phase Space of a Mechanical System 2. Representative Ensembles 3. The Liouville Equation 4. Formal Solution of the Liouville Equation 5. Non-Interacting Particles 6. Action-Angle Variables 7. Liouville’s Theorem in Action-Angle Variables 8. Liouville’s Equation in Interaction Representation 9. Example 10. Discussion of the Interaction Representation 11. Time-Dependent and Time-Independent Perturbation Theory

2. Anharmonic Solids

1. Hamiltonian 2. The Liouville Operator 3. Formal Solution for the Energy Distribution Function 4. Diagram Technique 5. Second-Order Contributions 6. Fourth-Order Contributions 7. Master Equation 8. H-Theorem 9. Fokker-Planck Equation and Master Equation

3. Brownian Motion

1. Basic Equations 2. Approach to Equilibrium 3. Statistical Theory of Brownian Motion 4. Evolution of the Fourier Components 5. Brownian Motion in Displacement and Velocity 6. Comparison with the Phenomenological Theory of Brownian Motion

4. Weakly Coupled Gases

1. Liouville Operator 2. Master Equation for Weakly Coupled Gases—Diagrams 3. Boltzmann Equation and Molecular Chaos 4. Explicit Form of the Boltzmann Equation 5. Brownian Motion 6. Fokker-Planck Equation and Dynamical Friction 7. Electrostatic Interactions — The Divergence Problem

5. Approach to Equilibrium in Weakly Coupled Gases

1. Introduction 2. H-Theorem 3. Disappearance of Inhomogeneities 4. Discussion

6. Scattering Theory and Short-Range Forces

1. Two-Body Scattering Theory 2. Propagators 3. Scattering in Phase Space 4. Equilibrium Distribution and Scattering Theory 5. iV-Body Problem in the Limit of Low Concentrations 6. Master Equation in the Limit of Low Concentrations 7. Scattering Theory and the N-Body Problem

7. Distribution Functions: The Diagram Representation

1. Distribution Functions 2. Fourier Expansion and Distribution Functions 3. Singularities in the Fourier Expansion 4. Cluster Expansion of the Distribution Functions 5. Physical Meaning of the Fourier Coefficients 6. Diagrams 7. Concentration Dependence of Diagrams 8. Reduced Distribution Functions and Diagrams

8. The Time Dependence of Diagrams

1. Effect of H0—Wave Packets 2. Duration of a Collision 3. Resolvent Method 4. Analytic Behavior of the Resolvent 5. Diagonal Fragments 6. Free Propagation and Scattering 7. Destruction of Correlations 8. Creation of Correlations 9. Propagation of Correlations 10. General Remarks about the Time Dependence of Diagrams 11. Velocity Distribution in Weakly Coupled or Dilute Systems 12. The Thermodynamic Case 13. Dynamics of Correlations and Time Dependence

9. Approach to Equilibrium in Ionized Gases

1. Choice of Diagrams 2. Summation of Rings 3. Solution of the Integral Equation 4. Discussion of the Transport Equation

10. Statistical Hydrodynamics

11. General Kinetic Equations

1. Evolution of the Velocity Distribution 2. Markowian Form of the Evolution Equation for the Velocity Distribution 3. Evolution of Correlations 4. Hydrodynamic Situations 5. Bogoliubov’s Theory 6. Stationary Non-Equilibrium States — Kinetic Equations and Time Scales

12. General H-Theorem

1. Introduction 2. Approach to Equilibrium of the Velocity Distribution Function 3. Approach to Equilibrium of the Correlations 4. Articulation Points and Principle of Detailed Balance 5. Two-Particle Correlation Function 6. Mechanism of Irreversibility

13. Quantum Mechanics

1. Quantum Mechanical Density Matrix 2. Quantum Mechanical Liouville Equation in Interaction Representation 3. Wave Vector Conservation 4. Pauli Equation

14. Irreversibility and Invariants of Motion

1. The condition of Dissipativity 2. Dissipativity and Poincaré’s Theorem 3. Analytic Invariants with singular Fourier Transforms 4. Approach to Equilibrium and Invariants

Appendix I: Laguerre Functions and Bessel Functions Appendix II: Derivation of the Master Equation by Time-Independent Perturbation Theory Appendix III: General Theory of Anharmonic Oscillators Appendix IV: Scattering by Randomly Distributed Centers and Van Hove’s Diagonal Singularity Conditions Bibliography List of Symbols Index