Nonequilibrium Statistical Physics

A Modern Perspective

Roberto Livi, Paolo Politi

• Publisher: Cambridge University Press
• Year: 2017
• Print ISBN: 9781107049543
• eBook ISBN: 9781108365086
• Topic: Physical Sciences
• Subtopic: Mathematical & Computational Physics

Statistical mechanics has been proven to be successful at describing physical systems at thermodynamic equilibrium. Since most natural phenomena occur in nonequilibrium conditions, the present challenge is to find suitable physical approaches for such conditions: this book provides a pedagogical pathway that explores various perspectives. The use of clear language, and explanatory figures and diagrams to describe models, simulations and experimental findings makes the book a valuable resource for undergraduate and graduate students, and also for lecturers organizing teaching at varying levels of experience in the field. Written in three parts, it covers basic and traditional concepts of nonequilibrium physics, modern aspects concerning nonequilibrium phase transitions, and application-orientated topics from a modern perspective. A broad range of topics is covered, including Langevin equations, Levy processes, directed percolation, kinetic roughening and pattern formation.

Table of contents

• Cover
• Half-title
• Title page
• Copyright information
• Dedication
• Table of contents
• Preface
• Acknowledgements
• Notations and Acronyms
• 1 Brownian Motion, Langevin and Fokker–Planck Equations
• 2 Linear Response Theory and Transport Phenomena
• 3 From Equilibrium to Out-of-Equilibrium Phase Transitions
• 4 Out-of-Equilibrium Critical Phenomena
• 5 Stochastic Dynamics of Surfaces and Interfaces
• 6 Phase-Ordering Kinetics
• 7 Highlights on Pattern Formation
• Appendix A The Central Limit Theorem and Its Limitations
• Appendix B Spectral Properties of Stochastic Matrices
• Appendix C Reversibility and Ergodicity in a Markov Chain
• Appendix D The Diffusion Equation and Random Walk
• Appendix E The Kramers–Moyal Expansion
• Appendix F Mathematical Properties of Response Functions
• Appendix G The Van der Waals Equation
• Appendix H The Ising Model
• Appendix I Derivation of the Ginzburg–Landau Free Energy
• Appendix J Kinetic Monte Carlo
• Appendix K The Mean-field Phase Diagram of the Bridge Model
• Appendix L The Deterministic KPZ Equation and the Burgers Equation
• Appendix M The Perturbative Renormalization Group for KPZ: A Few Details
• Appendix N The Gibbs–Thomson Relation
• Appendix O The Allen–Cahn Equation
• Appendix P The Rayleigh–Bénard Instability
• Appendix Q General Conditions for the Turing Instability
• Appendix R Steady States of the One-Dimensional TDGL Equation
• Appendix S Multiscale Analysis
• Index