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Absorbing phase transitions are an important class of nonequilibrium phase transitions. They are characterized by one or more absorbing states, defined as microscopic states from which the system cannot escape. The most famous case with one absorbing state is called directed percolation (a sort of driven version of the usual, isotropic percolation) and it represents, for example, the spreading of a disease through a contact process: If the infection rate is large enough with respect to the recovery rate, the asymptotic state shows a finite fraction of infected individuals. Models with one absorbing state, local dynamics, and no additional symmetries typically fall within the directed percolation universality class. We also provide a short introduction to self-organized criticality, devoting a section to the Bak–Tang–Wiesenfeld model.
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.
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