We investigate the main features of a pilot wave representation of the nonlinear Schrödinger equation recently advanced by Nobre, Rego-Monteiro, and Tsallis (NRT) on the basis of Tsallis q-thermo-statistical formalism. The present approach sheds new light upon the NRT equation. In particular,...

We study nonextensive statistical scenarios à la Tsallis with reference to Fisher’s information and Rènyi’s entropy. A new way of evaluating Tsallis’ generalized expectation values is examined within such a context, and is shown to lead to a much better Cramer–Rao bound than the...

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 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...

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...

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....

Bacry [Phys. Lett. B 317 (1993) 523] showed that, on the basis of the deformed Poincaré group, special relativity yields a non-additive energy for large systems, i.e., a total energy (of the Universe) which would not be proportional to the number of particles. He consistently argued that this...