Nonlinear Nonequilibrium Thermodynamics I - Linear and Nonlinear Fluctuation-Dissipation Theorems

This book gives the first detailed coherent treatment of a relatively young branch of statistical physics - nonlinear nonequilibrium and fluctuation-dissipative thermo dynamics. This area of research has taken shape fairly recently: its development began in 1959. The earlier theory -linear nonequilibrium thermodynamics - is in principle a simple special case of the new theory. Despite the fact that the title of this book includes the word "nonlinear", it also covers the results of linear nonequilibrium thermodynamics. The presentation of the linear and nonlinear theories is done within a common theoretical framework that is not subject to the linearity condition. The author hopes that the reader will perceive the intrinsic unity of this discipline, and the uniformity and generality of its constituent parts. This theory has a wide variety of applications in various domains of physics and physical chemistry, enabling one to calculate thermal fluctuations in various nonlinear systems. The book is divided into two volumes. Fluctuation-dissipation theorems (or relations) of various types (linear, quadratic and cubic, classical and quantum) are considered in the first volume. Here one encounters the Markov and non-Markov fluctuation-dissipation theorems (FDTs), theorems of the first, second and third kinds. Nonlinear FDTs are less well known than their linear counterparts.

List of contents

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. Fluctuation-Dissipation 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 Space-Time Spectral Densities.- A6.3 Spectral Density of Spatial Spectra and Space-Time 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.

Product details

• Authors: Rouslan L Stratonovich, Rouslan L. Stratonovich
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 05.12.2012
• EAN: 9783642773457
• ISBN: 978-3-642-77345-7
• No. of pages: 361
• Dimensions: 170 mm x 242 mm x 20 mm
• Weight: 655 g
• Illustrations: XVI, 361 p.
• Series: Springer Series in Synergetics; Springer Series in Synergetics
• Subject: Natural sciences, medicine, IT, technology > Physics, astronomy > Thermodynamics