We show that effective masses in nonrelativistic quantum mechanics arise in a natural fashion from the Frieden and Soffer's Principle of Extremal Information (EPI) when the mean values of operators involving the momentum p̂ and exhibiting the form p̂f(x̂)p̂ are included as constraints. A...

The recent proposal by Tsallis of a generalized thermostatistics devised to treat systems endowed with long-range interactions, long-range memory effects, or a fractal-like relevant phase space, has raised interesting and profound issues concerning the properties of general thermostatistical...

In this work, we analyze two important stochastic processes, the fractional Brownian motion and fractional Gaussian noise, within the framework of the Tsallis permutation entropy. This entropic measure, evaluated after using the Bandt & Pompe method to extract the associated probability...

Given a set of non-commuting operators Ô1,…,ÔN, and the assumed knowledge of the expectation values of a subset containing just M of them, we discuss, in quite general terms, what can be predicted about the behaviour of the expectation values of the remaining operators when the concomitant...

The level of order R in a spherical system of radius r0 with a probability amplitude function ψ(x),x=r,θ,ϕ obeys R=(1/2)r02I, where I=4∫dx|∇ψ|2 is its Fisher information level. We show that a flat space universe obeying the Robertson–Walker metric has an invariant value of the order as...

A principled framework to generalize variational perturbation approximations (VPAs) formulated within the ambit of the nonadditive statistics of Tsallis statistics, is introduced. This is accomplished by operating on the terms constituting the perturbation expansion of the generalized free...

We focus attention on the particular thermodynamic relation dU=TdS+δW. Using information theory concepts we show that, for a reversible process in which intensive variables change, microscopic considerations related to this thermodynamic relation make the informational contents of,...

We use Tsallis’ information measure and the recently advanced “escort-Tsallis” one in order to investigate the stochastic resonance (SR) phenomenon. In particular, on the basis of these generalized information measures (GIM), both characterized by a non-extensivity parameter q, we study...

By considering a simple thermodynamic system, in thermal equilibrium at a temperature T and in the presence of an external parameter A, we focus our attention on the particular thermodynamic (macroscopic) relation dU=TdS+δW. Using standard axioms from information theory and the fact that the...

It is well known that a suggestive relation exists that links the Schrödinger equation (SE) to the information-optimizing principle based on the Fisher information measure (FIM). We explore here an approach that will allow one to infer the optimal FIM compatible with a given amount of prior...