Nonequilibrium Statistical Physics: A Modern Perspective

EAN: 9781107049543
Published: 05/10/2017
Language: English

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.

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. Central limit theorem and its limitations
Appendix B. Spectral properties of stochastic matrices
Appendix C. Reversibility and ergodicity in a Markov chain
Appendix D. Diffusion equation and random walk
Appendix E. 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. Mean-field phase diagram of the bridge model
Appendix L. The deterministic KPZ 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.