Statistical Physics II

This volume of Statistical Physics consititutes the second part of Statistical Physics (Springer Series in Solid-State Science, Vols. 30, 31) and is devoted to nonequilibrium theories of statistical mechanics. We start with an intro­ duction to the stochastic treatment of Brownian motion and then proceed to general problems involved in deriving a physical process from an underlying more basic process. Relaxation from nonequilibrium to equilibrium states and the response of a system to an external disturbance form the central problems of nonequilibrium statistical mechanics. These problems are treated both phenomenologically and microscopically along the lines of re­ cent developments. Emphasis is placed on fundamental concepts and methods rather than on applications which are too numerous to be treated exhaustively within the limited space of this volume. For information on the general aim of this book, the reader is referred to the Foreword. For further reading, the reader should consult the bibliographies, although these are not meant to be exhaustive.

1. Brownian Motion. - 1. 1 Brownian Motion as a Stochastic Process. - 1. 2 Central Limit Theorem and Brownian Motion. - 1. 3 Langevin Equation and Harmonic Analysis. - 1. 4 Gaussian Processes. - 1. 5 Brownian Motion Modeled by a Gaussian Process. - 1. 6 Fluctuation-Dissipation Theorem. - 2. Physical Processes as Stochastic Processes. - 2. 1 Random Frequency Modulation. - 2. 2 Brownian Motion Revisited. - 2. 3 Markovian Processes. - 2. 4 Fokker-Planck Equation. - 2. 5 Contraction of Information. Projected Processes. - 2. 6 Derivation of Master Equations. - 2. 7 Brownian Motion of a Quantal System. - 2. 8 Boltzmann Equation. - 2. 9 Generalized Langevin Equation and the Damping Theory. - 3. Relaxation and Resonance Absorption. - 3. 1 Linear Irreversible Processes. - 3. 2 Complex Admittance. - 3. 3 Debye Relaxation. - 3. 4 Resonance Absorption. - 3. 5 Wave Number-Dependent Complex Admittance. - 3. 6 Dispersion Relations. - 3. 7 Sum Rules and Interpolation Formulas. - 4. Statistical Mechanics of Linear Response. - 4. 1 Static Response to External Force. - 4. 2 Dynamic Response to External Force. - 4. 3 Symmetry and the Dispersion Relations. - 4. 4 Fluctuation and Dissipation Theorem. - 4. 5 Density Response, Conduction and Diffusion. - 4. 6 Response to Thermal Internal Forces. - 4. 7 Some Remarks on the Linear-Response Theory. - 5. Quantum Field Theoretical Methods in Statistical Mechanics. - 5. 1 Double-Time Green s Functions. - 5. 2 Chain of Equations of Motion and the Decoupling Approximation. - 5. 3 Relation to the Kinetic Equation. - 5. 4 Single-Particle Green s Function and the Causal Green s Function. - 5. 5 Basic Formula for Perturbational Expansion. - 5. 6 Temperature Green s Function. - 5. 7 Diagram Technique. - 5. 8 Dyson Equation. - 5. 9 Relationship Between the Thermodynamic Potential and the Temperature Green s Function. - 5. 10Special Case of Two-Particle Green s Function. - General Bibliography of Textbooks. - References.