Elements of Nonequilibrium Statistical Mechanics

V. Balakrishnan

• Publisher: Springer
• Year: 2020
• Topic: Physical Sciences
• Print ISBN:
  9783030622329
• Subtopic: Industrial & Technical Chemistry
• eBook ISBN:
  9783030622336

This book deals with the basic principles and techniques of nonequilibrium statistical mechanics. The importance of this subject is growing rapidly in view of the advances being made, both experimentally and theoretically, in statistical physics, chemical physics, biological physics, complex systems and several other areas.  The presentation of topics is quite self-contained, and the choice of topics enables the student to form a coherent picture of the subject. The approach is unique in that classical mechanical formulation takes center stage. The book is of particular interest to advanced undergraduate and graduate students in engineering departments.

Table of contents

• Preface
• Acknowledgments
• Contents
• Prologue
• Chapter 1 Introduction
• Chapter 2 The Langevin equation
• Chapter 3 The fluctuation-dissipation relation
• Chapter 4 The velocity autocorrelation function
• Chapter 5 Markov processes
• Chapter 6 The Fokker-Planck equation and the Ornstein-Uhlenbeck distribution
• Chapter 7 The diffusion equation
• Chapter 8 Diffusion in a finite region
• Chapter 9 Brownian motion
• Chapter 10 First-passage time
• Chapter 11 The displacement of the tagged particle
• Chapter 12 The Fokker-Planck equation in phase space
• Chapter 13 Diffusion in an external potential
• Chapter 14 Diffusion in a magnetic field
• Chapter 15 Kubo-Green formulas
• Chapter 16 Mobility as a generalized susceptibility
• Chapter 17 The generalized Langevin equation
• Epilogue
• Appendix A Gaussian integrals
• Appendix B The gamma function
• Appendix C Moments, cumulants and characteristic functions
• Appendix D The Gaussian or normal distribution
• Appendix E From random walks to diffusion
• Appendix F The exponential of a (2 x 2) matrix
• Appendix G Velocity distribution in a magnetic field
• Appendix H The Wiener-Khinchin Theorem
• Appendix I Classical linear response theory
• Appendix J Power spectrum of a random pulse sequence
• Appendix K Stable distributions
• Suggested Reading
• Index