We show how the demon of Frieden and Soffer, working in a nonextensive statistical scenario, is able to devise solutions to some of Einstein’s field equations by recourse to nonlocal changes of variables between appropriate differential equations. It is seen that a variety of cosmological...

Escort distributions are a well established but (for physicists) a relatively new concept that is rapidly gaining wide acceptance in world. In this work we wish to revisit the concept within the strictures of the celebrated semiclassical Husimi distributions (HDs) and thereby investigate the...

We discuss here the use of generalized forms of entropy, taken as information measures, to characterize phase transitions and critical behavior in thermodynamic systems. Our study is based on geometric considerations pertaining to the space of parameters that describe statistical mechanics...

We generate a family of phase space, thermal coherent-state’s representations, within the framework of Tsallis’ Generalized Statistical Mechanics and study their properties. Our protagonists are q-gaussian distributions. We obtain analytical expressions for the most important...

In connection with Tsallis' generalized statistical mechanics, we discuss the associated quantal distribution functions and show, by recourse to elementary considerations, that nonextensivity entails apparent violations to the Pauli principle. The typical zero temperature sharp Fermi surface is...

We discuss some interesting peculiarities of Tsallis' quantum thermostatistics in relation with dynamical evolution, with particular emphasison the cut-off condition question. The existence of special dynamical states that do not appear in the Boltzmann-Gibbs thermostatics is analyzed in detail.

We discuss applying the increasingly popular q-calculus, or deformed calculus, so as to suitably generalize Fisher’s information measure and the Cramer–Rao inequality. A q-deformation can be attained in multiple ways, and we show that most of them do not constitute legitimate procedures....

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’...

As a part of the so-called Wheeler program, we present an information theoretic treatment for phase space distributions.

Fisher's information measures, as adapted to a nonextensive (Tsallis) environment, are discussed. For systems of particles that are in a general state of motion a lower bound to these information measures is derived with the help of a recently established upper bound to the entropy increase....