Nonextensive statistical mechanics: A brief introduction

Introduction to Nonextensive Statistical Mechanics

Introduction to Nonextensive Statistical Mechanics and Thermodynamics *

In this lecture we briefly review the definition, consequences and applications of an entropy, Sq, which generalizes the usual Boltzmann-Gibbs entropy SBG (S1 = SBG), basis of the usual statistical mechanics, well known to be applicable whenever ergodicity is satisfied at the microscopic dynamical level. Such entropy Sq is based on the notion of q-exponential and presents properties not shared ...

Nonextensive statistical mechanics: a brief review of its present status

We briefly review the present status of nonextensive statistical mechanics. We focus on (i) the central equations of the formalism, (ii) the most recent applications in physics and other sciences, (iii) the a priori determination (from microscopic dynamics) of the entropic index q for two important classes of physical systems, namely low-dimensional maps (both dissipative and conservative) and ...

Duality in nonextensive statistical mechanics.

We revisit recent derivations of kinetic equations based on Tsallis' entropy concept. The method of kinetic functions is introduced as a standard tool for extensions of classical kinetic equations in the framework of Tsallis' statistical mechanics. Our analysis of the Boltzmann equation demonstrates a remarkable relation between thermodynamics and kinetics caused by the deformation of macroscop...

Nonextensive statistical mechanics and economics

Ergodicity, this is to say, dynamics whose time averages coincide with ensemble averages, naturally leads to Boltzmann-Gibbs (BG) statistical mechanics, hence to standard thermodynamics. This formalism has been at the basis of an enormous success in describing, among others, the particular stationary state corresponding to thermal equilibrium. There are, however, vast classes of complex systems...