Statistical Mechanics Part B: Time-Dependent Processes

The last decade has been marked by a rapid growth in statistical mechanics, especially in connection with the physics and chemistry of the fluid state. Our understanding in these areas has been considerably advanced and enriched by the discovery of new techniques and the sharpening of old techniques, ranging all the way from computer simulations to mode-mode coupling theories. Statistical mechanics brings together under one roof a broad spectrum of mathematical methods. The aim of these volumes is to provide a didactic treatment of those topics that are most useful for the study of problems of current interest to theoretical chemists. The emphasis throughout is on the techniques themselves and not on reviewing the enormous literature in statistical mechanics. Each author was charged with the following task. Given N pages, (a) pose the problem, (b) present those aspects of the particular technique that cJearly illustrate its internal workings, (c) apply the technique to the solUlion of several illustrative examples, and (d) write the chapter so that it will enable the reader to approach key citations to the literature intelligently. These volumes are designed for graduate students and research workers in statistical mechanics. Nevertheless, they should be useful in other areas as weIl.

1. Molecular Dynamics Techniques for Hard-Core Systems.- 1. Introduction.- 2. Statistical-Mechanical Background.- 3. Approach to Equilibrium.- 4. Equilibrium Thermodynamic Functions.- 5. Equilibrium Time Correlation Functions.- 6. Nonequilibrium Molecular Dynamics.- 7. Accuracy of Molecular Dynamics Trajectory.- 8. Programming Techniques.- References.- 2. Molecular Dynamics Methods: Continuous Potentials.- 1. Introduction.- 2. Integration Procedures for the Equations of Motion.- 3. Time-Saving Techniques.- 4. Potential Functions for Anisotropic Molecules.- 5. The Calculation of Time Correlation Functions and Static Properties.- 6. Systems with Long-Range Forces.- 7. Brownian Molecular Dynamics.- 8. Conclusion.- References.- 3. The Kinetic Theory of Gases.- 1. Introduction.- 2. The Boltzmann Equation.- 3. The Kinetic Theory of Dense Gases.- 4. Time Correlation Functions.- 5. Discussion.- References.- 4. Renormalized Kinetic Theory of Dense Fluids.- 1. Introduction.- 2. Phase Space Time Correlation Functions.- 3. The Memory Function Formulation.- 4. Symmetrized Two-Particle Correlations with Renormalized Interactions.- 5. The Boltzmann-Enskog Theory of Thermal Fluctuations.- 6. The Velocity Autocorrelation Function of a Dense Fluid.- 7. Summary and Discussions.- Appendix A.- Appendix B.- Appendix C. Reduction of the Memory Function in the Boltzmann-Enskog Approximation.- References.- 5. Projection Operator Techniques in the Theory of Fluctuations.- 1. Introduction.- 2. Liouville Space.- 3. Relaxation Equations.- 4. Symmetry Properties.- 5. Navier-Stokes Equations.- 6. Conclusions.- References.- 6. Principles of Mode-Mode Coupling Theory.- 1. Introduction.- 2. Writing Mode-Mode Equations.- 3. Solving Mode-Mode Equations.- 4. Examples.- 5. Conclusion.- References.- 7. Global Analysis of Nonlinear Chemical Kinetics.- 1. Introduction.- 2. An Index Theorem for Chemical Kinetics.- 3. Flow Box Analysis in Chemical Kinetics.- 4. Some Limit Cycle Oscillations in Nonlinear Kinetic Equations.- 5. Reaction and Diffusion in a Ring of Cells.- 6. Discussion.- References.- Author Index.