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The first part of the chapter is a not-so-small presentation of equilibrium phase transitions, which allows us to introduce key concepts for both equilibrium and nonequilibrium phase transitions. The lattice gas, that is, the Ising model with a conserved order parameter, is an appropriate model to analyze how an equilibrium model can be brought out of equilibrium and to highlight the importance of boundary conditions in nonequilibrium phase transitions. The driven lattice gas, introduced by Katz, Lebowitz, and Spohn around 40 years ago, allows to define the totally asymmetric simple exclusion (TASEP) model and subsequently also the BRIDGE model. The latter is a one-dimensional model displaying a nonequilibrium phase transition with a symmetry breaking between two equivalent classes of particles. This result, considering the short-range character of interactions, would not be possible at equilibrium. In an equally unexpected way, an external breaking of the symmetry (equivalent to the application of a magnetic field to the Ising model) does not make the phase transition disappear.
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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