In the last two decades, the nonextensive statistics proposed by Tsallis have been extensively discussed in terms of the Tsallis entropy, which is a generalization of the Boltzmann–Gibbs–Shannon entropy. Within the nonextensive framework, many kinds of generalizations have been made. Suyari...

Stochastic bistable systems whose stationary distributions belong to the q-exponential family are investigated using two approaches: (i) the Langevin model subjected to additive and quadratic multiplicative noise, and (ii) the superstatistical model. Previously, the bistable Langevin model has...

The propagation of electron Bernstein waves in a magnetized plasma is investigated in the context of nonextensive q-distribution of Tsallis statistics. The dispersion relation is expressed as a function of generalized hypergeometric function. It is shown that the generalized dispersion relation...

A necessary precondition for modeling financial markets is a complete understanding of their statistics, including dynamics. Distributions derived from nonextensive Tsallis statistics are closely connected with dynamics described by a nonlinear Fokker–Planck equation. The combination shows...

The real distributions of local wind speed obtained from random temporal series have been analyzed in the framework of the new Eigen-coordinates method (ECs), which helps to identify a true hypothesis with high level of authenticity. The season variations of the wind speed have been registered...

Measurements in turbulent flows have revealed that the velocity field in nonequilibrium systems exhibits q-exponential or power-law distributions in agreement with theoretical arguments based on nonextensive statistical mechanics. Here we consider Hele–Shaw flow as simulated by the lattice...

Nonextensive statistical distributions suggested by Tsallis are studied in the framework of the so-called eigencoordinates (ECs) method which allows to recognize them with high level of authenticity. At first, the possibilities of the ECs method have been demonstrated on model files to exhibit...

This paper introduces a new hybrid approach for learning systems that builds on the theory of nonextensive statistical mechanics. The proposed learning scheme uses only the sign of the gradient, and combines adaptive stepsize local searches with global search steps that make use of an annealing...

Modern analyses of diffusion processes have proposed nonlinear versions of the Fokker–Planck equation to account for nonclassical diffusion. These nonlinear equations are usually constructed on a phenomenological basis. Here, we introduce a nonlinear transformation by defining the q-generating...

We present a stability analysis of the classical ideal gas in a new theory of nonextensive statistics and use this theory to understand the phenomena of negative specific heat in the nonextensive gas. The stability analysis is made on the basis of the second variation of Tsallis entropy. It is...