The standard q-Fourier Transform (qFT) of a constant diverges, which begs for a better treatment. In addition, Hilhorst has conclusively proved that the ordinary qFT is not of a one-to-one character for an infinite set of functions [H.J. Hilhorst, J. Stat. Mech. (2010) P10023]. Generalizing 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.

An exactly solvable quantum many-fermion system with an arbitrarily strong two-body interaction is studied and some exact thermodynamic functions (in the thermodynamic limit) are derived within the framework of the statistical inference scheme based on information theory. The solution for the...

We undertake the study of signals originated in time-dependent nonlinear systems by recourse to a wavelet-based multiresolution analysis as adapted to a nonextensive (Tsallis) scenario. Diverse applications are discussed. It is shown that the Tsallis environment provides one with more detailed...

In 1948 Shannon advanced information theory (IT) as a new branch of mathematics and a powerful tool for understanding the intricacies of the communication process. Nine years later Jaynes’ conceived the maximum entropy principle and was able to shed with it much light onto statistical...

The recently introduced approach for Encrypted Image Folding is generalized to make it self-contained. The goal is achieved by enlarging the folded image so as to embed all the necessary information for the image recovery. The need for extra size is somewhat compensated by considering a...

The statistical distribution, when determined from an incomplete set of constraints, is shown to be suitable as host for encrypted information. We design an encoding/decoding scheme to embed such a distribution with hidden information. The encryption security is based on the extreme instability...

We show, starting from first principles, that thermodynamics’ first law can be microscopically obtained for Fisher's information measure without need of invoking the adiabatic theorem. Further, it is proved that enforcing the Fisher-first law requirements in a process in which the probability...

Thermodynamics’ first law (TFL), although undoubtedly true because of its many verified consequences, rests on a rather weak experimental foundation in the sense that, as pointed out by Pippard, its path-independent aspect cannot be said to have been directly verified. From the theoretical...

There exist two different versions of the Kullback–Leibler divergence (K–Ld) in Tsallis statistics, namely the usual generalized K–Ld and the generalized Bregman K–Ld. Problems have been encountered in trying to reconcile them. A condition for consistency between these two generalized...