Foundations of Statistical Mechanics: Volume II: Nonequilibrium Phenomena

ISBN-13: 9789401077972 / Angielski / Miękka / 2011 / 307 str.

Jr. W. T. Grandy

Opis

In this volume we continue the logical development of the work begun in Volume I, and the equilibrium theory now becomes a very special case of the exposition presented here. Once a departure is made from equilibrium, however, the problems become deeper and more subtle-and unlike the equilibrium theory, many aspects of nonequilibrium phenomena remain poorly understood. For over a century a great deal of effort has been expended on the attempt to develop a comprehensive and sensible description of nonequilibrium phenomena and irreversible processes. What has emerged is a hodgepodge of ad hoc constructs that do little to provide either a firm foundation, or a systematic means for proceeding to higher levels of understanding with respect to ever more complicated examples of nonequilibria. Although one should rightfully consider this situation shameful, the amount of effort invested testifies to the degree of difficulty of the problems. In Volume I it was emphasized strongly that the traditional exposition of equilibrium theory lacked a certain cogency which tended to impede progress with extending those considerations to more complex nonequilibrium problems. The reasons for this were adduced to be an unfortunate reliance on ergodicity and the notions of kinetic theory, but in the long run little harm was done regarding the treatment of equilibrium problems. On the nonequilibrium level the potential for disaster increases enormously, as becomes evident already in Chapter 1.

Spis treści

Prologue.- References.- 1 The Equations of Classical Hydrodynamics.- A. Rheology.- B. The Conventional Microscopic Connection.- Transport Coefficients.- C. Thermodynamics.- D. Critique.- Problems.- References.- 2 General Theory of Nonequilibria.- A. Theory of the Partition Functional.- References.- 3 Theory of Dynamical Response.- A. Response Functions.- B. Linear Response and Fluctuations.- C. The Scope of Linear Response Theory.- Problems.- References.- 4 Dynamical Response of Real Systems.- Electric Fields.- Magnetic Fields.- A. Magnetic Polarization.- B. Electric Polarization.- C. Electrical Conductivity.- D. Gyromagnetic Phenomena.- E. Galvanomagnetic Effects.- F. Nonlinear Electromagnetic Response.- Problems.- References.- 5 General Nonequilibrium Processes.- A. Theory of the Steady State.- B. The Linear Approximation.- Comparison with Linear Dynamic Response.- C. Higher-Order Terms.- Problems.- References.- 6 Analysis of Covariance Functions for Simple Fluids.- A. General Properties of Covariance Functions.- Limiting Forms.- B. Calculation of Covariance Functions.- Perturbation Theory.- Free-Particle Covariance Functions.- Summary.- Problems.- References.- 7 Thermally Driven Systems.- A. Theory of Thermal Driving.- Mode Coupling.- Entropy.- Relation to Dynamical Driving.- B. Relaxation Processes.- Time-Decay of Covariance Functions.- Problems.- References.- 8 Transport Processes and Hydrodynamics.- A. Linear Transport Processes.- Particle Diffusion.- Thermal Conductivity.- Viscoelasticity.- B. Thermomechanical Processes.- Thermoelectric Phenomena.- Thermomagnetic Effects.- C. The Equations of Hydrodynamics.- D. The Hydrodynamic Limit.- Transport Coefficients.- Structure of Covariance Functions.- Problems.- References.- 9 Sound Propagation and Attenuation.- A. The Classical Theory of Sound.- Microscopic Connection.- B. Linear Theory of Sound Propagation and Attenuation.- Some General Considerations.- C. Ideal Gases, I: Boltzmann Statistics.- Physical Interpretation.- An Interaction Model.- D. Ideal Gases, II: Quantum Statistics.- Landau Theory of the Fermi Liquid.- Problems.- References.- Epilogue.- Nonlinearities.- Irregular Motion.- References.- Appendix A Operator Calculus and Identities.- Operator Identities.- Time-Evolution Operators.- References.- Appendix B Diagrammatic Analysis of Covariance Functions.- Self-Energy Analysis.- Interaction Models.- Ring Diagrams.- Ladder Diagrams.- Generalized Vertices.- References.- Appendix C The Density Covariance Function.- Summation of Ring Diagrams.- Ladder Sum and Hard Spheres.- References.