Statistical dynamics : matter out of equilibrium / Radu Balescu.

Format:

Book

Author/Creator:

Balescu, Radu.

Language:

English

Subjects (All):

Stochastic processes.

Probabilities.

Physical Description:

1 online resource (340 p.)

Place of Publication:

London : Imperial College Press, 2000, c1997.

Language Note:

English

Summary:

In the first part of this book, classical nonequilibrium statistical mechanics is developed. Starting from the Hamiltonian dynamics of the molecules, it leads through the irreversible kinetic equations to the level of fluid mechanics. For simple systems, all the transport coefficients are determined by the molecular properties.The second part of the book treats complex systems that require a more extensive use of statistical concepts. Such problems, which are at the forefront of research, include: continuous time random walks, non-Markovian diffusion processes, percolation and related critical

Contents:

Contents; Chapter 1 Introduction; 1.1 Bibliographical Notes BN1; Chapter 2 States, Dynamical Functions, Evolution; 2.1 General Considerations; 2.2 Macroscopic Dynamical Systems; 2.3 Microscopic Dynamical Systems; 2.4 Systems of Interacting Particles; 2.5 Bibliographical Notes BN2; Chapter 3 General Formalism of Statistical Mechanics; 3.1 Macroscopic Physics and Microscopic Physics; 3.2 The Phase Space Distribution Function; 3.3 Equilibrium States; 3.4 Bibliographical Notes BN3; Chapter 4 Reduced Distribution Functions and Correlation Functions; 4.1 Classification of Dynamical Functions

4.2 Reduced Distribution Functions4.3 Evolution of the Reduced Distribution Functions; 4.4 Correlation Functions; 4.5 Evolution of the Correlation Functions; 4.6 Bibliographical Notes BN4; Chapter 5 The Mean Field Approximation; 5.1 Weakly Coupled Systems; 5.2 Free Particle Dynamics; 5.3 The Vlasov Equation; 5.4 The Linearized Vlasov Equation; 5.5 Conclusions; 5.6 Bibliographical Notes BN5; Chapter 6 The Weak Coupling Kinetic Equation; 6.1 The Master Equation; 6.2 The Landau Equation; 6.3 Explicit form of the Landau collision term; 6.4 Conclusion; 6.5 Appendix. The Cauchy Integral

6.6 Bibliographical Notes BN6Chapter 7 Kinetic Equation for Dilute Gases; 7.1 The Dilute Gas Ordering; 7.2 The Boltzmann Equation; 7.3 Implementation of the Boltzmann Equation; 7.4 Bibliographical Notes BN7; Chapter 8 Kinetic Equation for Plasmas; 8.1 The Plasma Ordering; 8.2 The Integral Equation for the Correlation; 8.3 The Plasma Kinetic Equation; 8.4 Properties of the Balescu-Lenard Equation; 8.5 Bibliographical Notes BN8; Chapter 9 Properties of Kinetic Equations; 9.1 The Concept of a Kinetic Equation; 9.2 Stochastic Equations of Evolution; 9.3 Nature of the Collision Process

9.4 Irreversibility and Entropy9.5 Spatially Inhomogeneous Systems; 9.6 The Collisional Invariants; 9.7 Bibliographical Notes BN9; Chapter 10 Hydrodynamics and Transport; 10.1 The Hydrodynamic Quantities; 10.2 The Hydrodynamical Balance Equations; 10.3 Diffusion and Heat Conduction; 10.4 The Hermitian Moment Expansion; 10.5 Derivation of the Transport Equations; 10.6 Properties of the Transport Coefficients; 10.7 Entropy and Transport; 10.8 Conclusions; 10.9 Bibliographical Notes BN10; Chapter 11 Transport and Autocorrelation Functions; 11.1 Introduction

11.2 Mean Square Displacement and Diffusion11.3 The Langevin Equations; 11.4 The Hybrid Kinetic Equation; 11.5 The Green-Kubo Formulae; 11.6 Bibliographical Notes BN11; Chapter 12 Random Walks and Transport; 12.1 Classical Random Walks; 12.2 Continuous Time Random Walks (CTRW); 12.3 The Standard Long-Tail CTRW (SLT-CTRW); 12.4 SLT-CTRW: The Density Profile; 12.5 SLT-CTRW: The Non-Markovian Diffusion Equation; 12.6 Markovian vs. Non-Markovian Evolution; 12.7 Appendix. Stable Probability Distribution Functions; 12.8 Bibliographical Notes BN12; Chapter 13 Critical Phenomena

13.1 Overview of the Equilibrium Critical Phenomena

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9781848160958

184816095X