We construct classes of stochastic differential equations with fluctuating friction forces that generate a dynamics correctly described by Tsallis statistics and nonextensive statistical mechanics. These systems generalize the way in which ordinary Langevin equations underly ordinary statistical mechanics to the more general nonextensive case. As a main example, we construct a dynamical model o...

A family of entropy indices constructed in the framework of Tsallis entropy formalism is used to investigate ecological diversity. It represents a new perspective in ecology because a simple equation can incorporate all aspects of α−diversity, from richness to dominance and can be also related to a measure of species rarity. In addition, a generalized Kullback-Leibler distance, constructed in t...

The charge distribution of the heaviest fragment detected in the decay of quasiprojectiles produced in intermediate energy heavy-ion collisions has been observed to be bimodal. This feature is expected as a generic signal of phase transition in nonextensive systems. In this Letter, we present new analyses of experimental data from Au on Au collisions at 60, 80, and 100 MeV/nucleon showing that ...

Recently much attention has been paid to the nonextensive canonical distributions: the αfamilies. Such distributions have been found in many real-world systems such as fully developed turbulence and financial markets. In this paper, a generalized mean-field method to approximate the expectations of the α-families is proposed. We calculate the α′-projection of a probability distribution to find ...

It is well known that energy spectra of particles from atmospheric family events which are observed by the emulsion chambers at mountain altitudes are essentially following power-like dependence. On the other hand the occurence of power-law distributions is a very common feature in nature and it is usually connected with such notions as criticality, fractals and chaotic dynamics and studied usi...