Special Issue "Advances in Applied Statistical Mechanics"

There is a diffuse belief that statistical properties of physical systems are well described by Boltzmann­Gibbs statistical mechanics. However, a constantly increasing amount of situations are known to violate the predictions of orthodox statistical mechanics. Systems where these emerging features are observed seem do not fulfill the standard ergodic and mixing properties on which the Boltzmann-Gibbs formalism are founded. In general, these systems are governed by nonlinear dynamics which establishes a deep relation among the parts. As a consequence, they reach a dynamical equilibrium in which the equilibrium probability distribution can differ deeply from the exponential shape typical of the Gibbs distribution. In the last decades, we assisted to an intense research activity that has modified our understanding of statistical physics, extending and renewing its applicability considerably. Important developments, relating equilibrium and nonequilibrium statistical physics, kinetic theory, information theory and others, have produced a new understanding of the properties of complex systems that requires, in many cases, the extension of the theory beyond the Boltzmann-Gibbs formalism. The aim of this special issue, is to collect papers in both the foundations and the applications of Statistical Mechanics going outside its traditional application. In particular, foundations regard classical and quantum aspects of statistical physics including generalized entropies, free-scale distributions, information theory, geometry information, nonextensive statistical mechanics, kinetic theory, long-range interactions and small systems. Applications are different and may include biophysics, seismology, econophysics, social systems, physics of networks, physics of risk, traffic flow, complex systems, fractal systems and others.