The biparametric Fisher-Rényi complexity measure and its application to the multidimensional blackbody radiation

Abstract

We introduce a biparametric Fisher-Rényi complexity measure for general probability distributions and we discuss its properties. This notion, which is composed of two entropy-like components (the Rényi entropy and the biparametric Fisher information), generalizes the basic Fisher-Shannon measure and the previous complexity quantifiers of Fisher-Rényi type. Then, we illustrate the usefulness of this notion by carrying out a information-theoretical analysis of the spectral energy density of a $d$-dimensional blackbody at temperature $T$. It is shown that the biparametric Fisher-Rényi measure of this quantum system has a universal character in the sense that it does not depend on temperature nor on any physical constant (e.g., Planck constant, speed of light, Boltzmann constant), but only on the space dimensionality $d$. Moreover, it decreases when $d$ is increasing, but exhibits a non trivial behavior for a fixed $d$ and a varying parameter, which somehow brings up a non standard structure of the blackbody $d$-dimensional density distribution.

Accepted for publication in Journal of Statistical Mechanics: Theory and Experiment

References in corpus (5)

• A possible deformed algebra and calculus inspired in nonextensive thermostatistics
• Rényi entropies of the highly-excited states of multidimensional harmonic oscillators by use of strong Laguerre asymptotics
• Can one measure the Cosmic Neutrino Background?
• One-parameter Fisher-Rényi complexity: Notion and hydrogenic applications
• Heisenberg-like uncertainty measures for $D$-dimensional hydrogenic systems at large D

Cited by in corpus (1)

• On Generalized Stam Inequalities and Fisher-Rényi Complexity Measures