On nonextensive thermo-statistics: systematization, clarification of scope and interpretation, and illustrations

Abstract

When dealing with certain kind of complex phenomena the theoretician may face some difficulties -- typically a failure to have access to information for properly characterize the system -- for applying the full power of the standard approach to the well established, physically and logically sound, Boltzmann-Gibbs statistics. To circumvent such difficulties, in order to make predictions on properties of the system and looking for an understanding of the physics involved (for example in analyzing the technological characteristics of fractal-structured devices) can be introduced large families of auxiliary statistics. We present here a systematization of these different styles in what can be termed as Unconventional Statistical Mechanics, accompanied of an analysis of the construction and a clarification of its scope and interpretation. As illustrations are derived heterotypical Bose-Einstein, Fermi-Dirac and Maxwell-Boltzmann distributions, and several applications including studies of experimental works are briefly described.