Nonequilibrium Statistical Physics: A Modern Perspective

Statistical mechanics is hugely successful when applied to physical systems at thermodynamic equilibrium; however, most natural phenomena occur in nonequilibrium conditions and more sophisticated techniques are required to address this increased complexity. This second edition presents a comprehensive overview of nonequilibrium statistical physics, covering essential topics such as Langevin equations, Lévy processes, fluctuation relations, transport theory, directed percolation, kinetic roughening, and pattern formation. The first part of the book introduces the underlying theory of nonequilibrium physics, the second part develops key aspects of nonequilibrium phase transitions, and the final part covers modern applications. A pedagogical approach has been adopted for the benefit of graduate students and instructors, with clear language and detailed figures used to explain the relevant models and experimental results. With the inclusion of original material and organizational changes throughout the book, this updated edition will be an essential guide for graduate students and researchers in nonequilibrium thermodynamics.

Table of Contents:
Preface to the second edition; Acknowledgements; Notations and acronyms; 1. Kinetic theory and the Boltzmann equation; 2. Brownian motion, Langevin and Fokker–Planck equations; 3. Fluctuations and their probability; 4. Linear response theory and transport phenomena; 5. From equilibrium to out-of-equilibrium phase transitions: Driven lattice gases; 6. Absorbing phase transitions; 7. Stochastic dynamics of surfaces and interfaces; 8. Phase-ordering kinetics; 9. Highlights on pattern formation; Appendix A: Binary elastic collisions in the hard sphere gas; Appendix B: Maxwell-Boltzmann distribution in the uniform case; Appendix C: Physical quantities from the Boltzmann equation in the nonuniform Case; Appendix D: Outine of the Chapman-Enskog method; Appendix E: First-order approximation to Hydrodynamics; Appendix F: Spectral properties of stochastic matrices; Appendix G: The deterministic KPZ equation and the Burgers equation; Appendix J: Stochastic differential equation for the energy of the Brownian particle; Appendix K: The Kramers–Moyal expansion; Appendix L: Probability distributions; Appendix M: The diffusion equation and the Random Walk; Appendix N: Linear response in quantum systems; Appendix O: Mathematical properties of response functions; Appendix P: The Van der Waals equation; Appendix Q: Derivation of the Ginzburg–Landau free energy; Appendix R: The perturbative renormalization group for KPZ; Appendix S: TASEP: Map method and simulations; Appendix T: Bridge Model: Mean-field and simulations; Appendix U: The Allen–Cahn equation;  Appendix V: The Gibbs–Thomson relation; Appendix W: The Rayleigh–Bénard instability; Appendix X: General conditions for the Turing instability;  Appendix Y: Steady states of the one-dimensional TDGL equation;  Appendix Z: Multiscale analysis; Index.

About the Author :
Roberto Livi is Honorary Professor of Theoretical Physics at the University of Florence and an associate member of the National Institute of Nuclear Physics (INFN) and of the Institute for Complex Systems of the National Research Council (CNR). His research is focused on nonequilibrium statistical physics, and he has extensive experience teaching courses on statistical physics. He is the current President of the Italian Society of Statistical Physics. Paolo Politi is a Research Director at the Institute for Complex Systems of the National Research Council (CNR), and Fellow of the Marie Curie Association, the Alexander von Humboldt Foundation, and the Japan Society for the promotion of Science. He currently teaches a course on stochastic processes and nonequilibrium statistical physics at the University of Florence. He was awarded the Outreach Prize of the Italian Physical Society.

Review :
Praise for the First Edition: 'The smart organizational choices mean that readers can get a feeling for the physical concepts involved and where to find more information. Committed students can work through the whole book, and less patient readers can concentrate on one or two chapters at a time. Nonequilibrium Statistical Physics will be welcomed both by students and researchers entering the field and by those who are familiar with some recent developments and would like to learn more about others.' Daan Frenkel, University of Cambridge, UK 'Since the publication of the first edition, the textbook by Livi and Politi has become an indispensable resource for my courses on advanced and nonequilibrium statistical physics. The carefully restructured and expanded second edition covers a wealth of new material, from fundamentals such as the Boltzmann equation and large deviation theory to the emerging field of stochastic thermodynamics and fluctuation relations. It will be highly appreciated by coming generations of students, teachers, and researchers.' Joachim Krug, University of Cologne, Germany 'This masterful work is a gateway to understanding the dynamic, often chaotic, and always fascinating world of nonequilibrium systems.' Giorgio Parisi, Sapienza University of Rome, Italy