We consider a monoparametric family of reaction–diffusion equations endowed with both a nonlinear diffusion term and a nonlinear reaction one that possess exact time-dependent particular solutions of the Tsallis’ maximum entropy (MaxEnt) form. The evolution of these solutions is governed by...

A formal correspondence between the q-distribution obtained from the Tsallis entropy and non-Maxwellian distributions obtained from the Boltzmann–Gibbs (BG) entropy is obtained. This formal correspondence is obtained by imposing an infinite number of constraints when one maximizes the BG...

After considering the kinetical interaction principle (KIP) introduced by Kaniadakis (Physica A 296 (2001) 405), we study in the Boltzmann picture, the evolution equation and the H-theorem for non-extensive systems. The q-kinetics and the κ-kinetics are studied in detail starting from the most...

We propose a new model of cancer growth based on nonextensive entropy. The evolution equation depends on the nonextensive parameter q. The exponential, the logistic, and the Gompertz growth laws are particular cases of the generalized model. Experimental data of different tumors have been shown...

We show that bunch-particle interactions in accelerator beams via wakefields as predicted by the Haïssinski theory can be described by the nonextensive entropy proposed by Tsallis for the nonextensivity parameter ν=2. A new method to analyze the Haïssinski problem is proposed that yields...

A statistical measure of complexity utilising the concept of entropy or information is proposed. Our way in this study is to use a nonextensive entropy instead of an extensive (additive) Shannon entropy in the definition, but can be characterised as a difference between the qth-order Rényi...

Generalizing the group structure of the Euclidean space, we construct a Riemannian metric on the deformed set Rqn induced by the Tsallis entropy composition property. We show that the Tsallis entropy is a “hyperbolic analogue” of the “Euclidean” Boltzmann/Gibbs/Shannon entropy and find...

We propose a one-parameter family Rq of deformations of the reals, which is motivated by the generalized additivity of the Tsallis entropy. We introduce a generalized multiplication which is distributive with respect to the generalized addition of the Tsallis entropy. These operations establish...