Over the last couple of decades nonextensive Tsallis entropy has shown remarkable applicability to describe nonequilibrium physical systems with large variability and multifractal structure. Herein, we review recent results from the application of Tsallis statistical mechanics to the detection of dynamical changes related with the occurrence of magnetic storms. We extend our review to describe ...

Hawking radiation is one of the cores in modern gratitational theory. Several articles have calculated spectrum Boltzmann-Gibbs statistical mechanics. However, based on recent researches, gravitational systems cannot be studied by standard In this article, we calculate modification to Tsallis We obtain modified Stefan-Boltzmann's law and power radiation. confirm conclusion proposed Giddings, na...

We investigated two different approaches, which can be used to extend the standard quantum statistical mechanics. One is based on fractional calculus, and other considers extension of concept entropy, i.e., Tsallis statistics. reviewed discussed some main properties these approaches thermal Green function formalism perform developments, simultaneously allowing us analyze each case’s dynamics th...

It is shown that a recent proposal to give physically meaningful definitions of temperature and pressure within Tsallis formalism for non-extensive thermostatistics leads to expressions which coincide with those obtained by using the standard Boltzmann formalism of Statistical Mechanics.

It is often stated that heat baths with finite degrees of freedom i.e., finite baths, are sources of Tsallis distributions for classical Hamiltonian systems. By using well-known fundamental statistical mechanics expressions, we rigorously show that Tsallis distributions with fat tails are possible only for finite baths with constant negative heat capacity, while constant positive heat capacity ...

The statistical properties of fully developed hydrodynamic turbulence can be successfully described using methods from nonextensive statistical mechanics. The predicted probability densities and scaling exponents precisely coincide with what is measured in various turbulence experiments. As a dynamical basis for nonextensive behaviour we consider nonlinear Langevin equations with fluctuating fr...

Classical statistical mechanics of macroscopic systems in equilibrium is based on Boltzmann's principle. Tsallis has proposed a generalization of Boltzmann-Gibbs statistics. Its relation to dynamics and nonextensivity of statistical systems are matters of intensive investigation and debate. This essay review has been prepared at the occasion of awarding the 'Mexico Prize for Science and Technol...

For a paradigmatic case, the standard map, we discuss how the statistical description of the approach to equilibrium is related to the sensitivity to the initial conditions of the system. Using a numerical analysis we present an anomalous scenario that may give some insight on the foundations of the Tsallis’ statistical mechanics.

Space plasmas are frequently described by kappa distributions. Non-extensive statistical mechanics involves the maximization of the Tsallis entropic form under the constraints of canonical ensemble, considering also a dyadic formalism between the ordinary and escort probability distributions. This paper addresses the statistical origin of kappa distributions, and shows that they can be connecte...