Alternative definitions are given of basic concepts of generalized thermostatistics. In particular, generalizations of Shannon’s entropy, of the Boltzmann-Gibbs distribution, and of relative entropy are considered. Particular choices made in Tsallis’ nonextensive thermostatistics are questioned.

Bose-Einstein (BE) and Fermi-Dirac (FD) distributions in nonextensive quantum statistics have been discussed with the use of exact integral representations for the grand canonical partition function [Rajagopal, Mendes and Lenzi, Phys. Rev. Lett. 80, 3907 (1998)]. Integrals along real axis in the case of q > 1.0 are modified by an appropriate change of variable, which makes numerical calculation...

– We present an analysis of the statistical properties of hydrodynamic field fluctuations which reveal the existence of precursors to fingering processes. These precursors are found to exhibit power law distributions, and these power laws are shown to follow from spatial q-Gaussian structures which are solutions to the non-linear porous media equation. Over the past fifteen years, a nonextensiv...

The q-state Potts model with long-range interactions that decay as 1/r subjected to a uniform magnetic field on d-dimensional lattices is analyzed for different values of q in the nonextensive regime 0<a<d . We calculate the mean-field solution of the model for all q and performed, for some values of q, Monte Carlo simulations for the spontaneous magnetization in the one-dimensional case. We sh...