An introduction to stochastic processes and nonequilibrium statistical physics / Horacio S. Wio.

Format:

Book

Author/Creator:

Wio, Horacio S.

Series:

Series on Advances in Statistical Mechanics

Series on advances in statistical mechanics ; v. 10

Language:

English

Subjects (All):

Statistical physics.

Stochastic processes.

Nonequilibrium thermodynamics.

Physical Description:

1 online resource (232 p.)

Place of Publication:

Singapore ; River Edge, N.J. : World Scientific, c1994.

Language Note:

English

Summary:

The purpose of this textbook is to bring together, in a self-contained introductory form, the scattered material in the field of stochastic processes and statistical physics. It offers the opportunity of being acquainted with stochastic, kinetic and nonequilibrium processes. Although the research techniques in these areas have become standard procedures, they are not usually taught in the normal courses on statistical physics. For students of physics in their last year and graduate students who wish to gain an invaluable introduction on the above subjects, this book is a necessary tool.

Contents:

PREFACE; CONTENTS; CHAPTER I: STOCHASTIC PROCESSES AND THE MASTER EQUATION; I.1: Introduction; I.2: Stochastic Processes; 1.2.1 Distribution Functions and Mean Values; 1.2.2 Joint and Conditional Probabilities; I.3: Markovian Processes; I.4: Master Equation; I.5: Kramers-Moyal Expansion; I.6 : Brownian Notion, Langevin and Fokker-Planck Equations; I.7 : Van Kampen's Ω Expansion; I.8 : Limitations of the Ω Expansion; APPENDIX I.A : Approach to Equilibrium - Ehrenfest Urn Model (Dog-Flea Model); APPENDIX I.B : Stochastic Differential Equations and Fokker-Planck Equations

APPENDIX I.C : PATH-INTEGRAL FOR MARKOV PROCESSESCHAPTER II: DISTRIBUTIONS, BBGKY-HIERARCHY, BALANCE EQUATIONS, AND THE DENSITY OPERATOR; II.2 : Probability Density as a Fluid; II.3: BBGKY Hierarchy; II.4 SIMPLE KINETIC EQUATIONS : VLASOV AND BOLTZMANN; II.5 MICROSCOPIC BALANCE EQUATIONS; II.6 DENSITY OPERATOR; II.6 REDUCED DENSITY OPERATOR; APPENDIX II.A : H-THEOREM; APPENDIX II.B : TRANSPORT COEFFICIENTS; CHAPTER III: LINEAR NON-EQUILIBRIUM THERMODYNAMICS AND ONSAGER RELATIONS; III.1 : Introduction; III.2 Onsager Regression to Equilibrium Hypothesis.; III.3 Onsager Relations

III.4 Onsager's Relations Examples(a) MechanoChaloric Effect :; III.5 Minimum Production of Entropy.; Appendix III.A : Some Concepts of Fluctuations Around Equilibrium; CHAPTER IV: LINEAR RESPONSE THEORY, FLUCTUATION-DISSIPATION THEOREM; IV.1 : Introduction; IV.2 Correlation Functions : Definitions and Properties; a) PROPERTIES; b) SUM RULES; IV.3 : Linear Response Theory.; IV.3.a Inelastic Scattering Cross Section; IV.3.b Response Functions; IV.4 : Fluctuation-Dissipation Theorem, and Properties of Response Functions; IV.5 : Some Examples.; a) Dielectric Susceptibility :

b) Transport Coefficients :CHAPTER V : INSTABILITIES AND FAR FROM EQUILIBRIUM PHASE TRANSITIONS; V.1 : Introduction; V.2 : PHASE PLANE ANALYSIS AND LINEAR STABILITY IHEORY; V.3 : LIMIT CYCLES, BIFURCATIONS, SYMMETRY BREAKING.; V.4 : BISTABILITY, ESCAPE TIMES, CRITICAL PHENOMENA.; V.5 : NOISE INDUCED TRANSITIONS.; CHAPTER VI: FORMATION AND PROPAGATION OF PATTERNS IN FAR FROM EQUILIBRIUM SYSTEMS; VI.1 : Introduction; VI.2 : REACTION-DIFFUSION DESCRIPTIONS AND PATTERN FORMATION.; VI.3 : EXAMPLE : AN ELECTROTHERMAL INSTABILITY.; VI.4 : PATTERN PROPAGATION : (a) ONE COMPONENT SYSTEMS.

VI.5 : PATTERN PROPAGATION : (b) TWO COMPONENT SYSTEMS.VI.6 : THE GENESIS OF SPIRALS; FINAL COMMENTS; BIBLIOGRAPHY; a) GENERAL TEXTBOOKS :; b) SPECIALIZED TEXTBOOKS :; CHAPTER I; CHAPTER II; CHAPTER III; CHAPTER IV; CHAPTER V; CHAPTER VI

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 209-217).

ISBN:

9789814350280

9814350281