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An interface is rough if the mean square fluctuations of its position diverge at large times and system sizes. This may occur when the interface is driven out of equilibrium in the presence of some noise and the way roughness diverges defines suitable critical exponents. We introduce and discuss extensively two important universality classes: the Edwards–Wilkinson and the Kardar–Parisi–Zhang. The latter has been the subject of renewed interest since it was possible to determine analytically the whole spectrum of fluctuations and it was found an experimental system satisfying such predictions with great accuracy. The last part of the chapter is devoted to nonlocal models, specifically the celebrated Diffusion Limited Aggregation.
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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