The concept of Jeans gravitational instability is rediscussed in the framework of the nonextensive statistics proposed by Tsallis. A simple analytical formula generalizing the Jeans criterion is derived by assuming that the un-perturbed self-gravitating collisionless gas is described by the q-parametrized class of nonextensive velocity distribution. It is shown that the critical values of wavel...

A hybrid approach is described, which combines stochastic classical molecular dynamics and rst principles Density Functional theory to model the atomic and electronic structure of large molecular and solid-state systems. The stochastic molecular dynamics using Generalized Simulated Annealing (GSA) is based on the nonextensive statistical mechanics and thermodynamics. Examples are given of appli...

We study multivariate generalizations of the q-central limit theorem, a generalization of the classical central limit theorem consistent with nonextensive statistical mechanics. Two types of generalizations are addressed, more precisely the direct and sequential q-central limit theorems are proved. Their relevance to the asymptotic scale invariance of some specially correlated systems is studie...

Special Edition “2015 UN/Japan Workshop on Space Weather” 157 Pathway Model and Nonextensive Statistical Mechanics A.M. Mathai, H.J. Haubold , C. Tsallis 5 1 Department of Mathematics and Statistics, McGill University, Quebec, Canada 2 Centre for Mathematical and Statistical Sciences, Kerala, India 3 Office for Outer Space Affairs, United Nations, Vienna, Austria 4 Centro Brasileiro de Pesquisa...

We review a new form of entropy suggested by us, with origin in mixing of states of systems due to interactions and deformations of phase cells. It is demonstrated that this nonextensive form also leads to asymmetric maximal entropy configurations unlike Shannon entropy. We discuss how, beginning with quantum entanglement of microsystems with one another and with the environment, one can obtain...

Human object extraction from infrared image has broad applications, and has become an active research area in image processing community. Combined with chaos differential evolution (CDE) algorithm and morphological operators, a novel infrared human target extraction method is proposed based on nonextensive fuzzy entropy. Firstly, the image was transformed into a fuzzy domain by fuzzy membership...

An analysis of the thermodynamic behavior of quantum systems can be performed from a geometrical perspective investigating the structure of the state space. We have developed such an analysis for nonextensive thermostatistical frameworks, making use of the q-divergence derived from Tsallis’ entropy. Generalized expressions for operator variance and covariance are considered, in terms of which t...