Nonequilibrium Statistical Physics
A Modern Perspective

This second edition provides a modern and accessible overview of the foundations and applications of nonequilibrium statistical physics.

Roberto Livi (Author), Paolo Politi (Author)

9781316512302, Cambridge University Press

Hardback, published 3 July 2025

532 pages
25.4 x 17.8 x 2.9 cm, 1.243 kg

'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

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.

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.

Subject Areas: Statistical physics [PHS]