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Full Description
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.
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.
