This book gives the first detailed and coherent treatment of a young and exciting branch of statistical physics. Both theoretical physicists and applied scientists will find this material of interest since the theoretical treatment is supported by numerous illustrative examples and application of the general results to a variety of electrical, thermal, mechanical and chemical systems.

Inhalt

1. Introduction.- 1.1 What Is Nonlinear Nonequilibrium Thermodynamics?.- 1.2 Early Work on Nonlinear Nonequlibrium Thermodynamics.- 1.3 Some Particular Problems and Their Corresponding FDRs: Historical Aspects.- 2. Auxiliary Information Concerning Probability Theory and Equilibrium Thermodynamics.- 2.1 Moments and Correlators.- 2.2 Some Results of Equilibrium Statistical Thermodynamics.- 2.3 The Markov Random Process and Its Master Equation.- 2.4 Infinitely Divisible Probability Densities and Markov Processes.- 2.5 Notes on References to Chapter 2.- 3. The Generating Equation of Markov Nonlinear Nonequilibrium Thermodynamics.- 3.1 Kinetic Potential.- 3.2 Consequences of Time Reversibility.- 3.3 Examples of the Kinetic Potential and of the Validity of the Generating Equation.- 3.4 Other Examples: Chemical Reactions and Diffusion.- 3.5 Generating Equation for the Kinetic Potential Spectrum.- 3.6 Notes on References to Chapter 3.- 4. Consequences of the Markov Generating Equation.- 4.1 Markov FDRs.- 4.2 Approximate Markov FDRs and Their Covariant Form.- 4.3 Application of FDRs for Approximate Determination of the Coefficient Functions.- 4.4 Examples of the Application of Linear Nonequilibrium Thermodynamics Relations.- 4.5 Examples of the Application of the Markov FDRs of Nonlinear Nonequilibrium Thermodynamics.- 4.6 H-Theorems of Markov Nonequilibrium Thermodynamics.- 4.7 Notes on References to Chapter 4.- 5. FluctuationDissipation Relations of Non-Markov Theory.- 5.1 Non-Markov Phenomenological Relaxation Equations and FDRs of the First Kind.- 5.2 Definition of Admittance and Auxiliary Formulas.- 5.3 Linear and Quadratic FDRs of the Second Kind.- 5.4 Cubic FDRs of the Second Kind.- 5.5 Connection Between FDRs of the First and Second Kinds.- 5.6 Linear and Quadratic FDRs of the Third Kind.- 5.7 Cubic FDRs of the Third Kind.- 5.8 Notes on References to Chapter 5.- 6. Some Uses of Non-Markov FDRs.- 6.1 Calculation of Many-Time Equilibrium Correlators and Their Derivatives in the Markov Case.- 6.2 Examples of Computations of Many-Fold Correlators or Spectral Densities and Their Derivatives with Respect to External Forces.- 6.3 Other Uses of Nonlinear FDRs.- 6.4 Application of Cubic FDRs to Calculate Non-Gaussian Properties of Flicker Noise.- 6.5 Notes on the References to Chapter 6.- Appendices.- A1. Relation of Conjugate Potentials in the Limit of Small Fluctuations.- A2. On the Theory of Infinitely Divisible Probability Densities.- A2.1 Justification of the Representation (2.4.9) Subject to (2.4.10).- A2.2 Example: Gaussian Distribution.- A3. Some Formulas Concerning Operator Commutation.- A5. The Contribution of Individual Terms of the Master Equation.- A6. Spectral Densities and Related Formulas.- A6.1 Definition of Many-Fold Spectral Densities.- A6.2 SpaceTime Spectral Densities.- A6.3 Spectral Density of Spatial Spectra and SpaceTime Spectral Density.- A6.4 Spectral Density of Nonstationary and Nonhomogeneous Random Functions.- A7. StochasticEquations for the Markov Process.- A7.1 The Ito Stochastic Equation.- A7.2 Symmetrized Stochastic Equations.- References.