Entropy and complexity properties of the d-dimensional blackbody radiation

Abstract

Space dimensionality is a crucial variable in the analysis of the structure and dynamics of natural systems and phenomena. The dimensionality effects of the blackbody radiation has been the subject of considerable research activity in recent years. These studies are still somewhat fragmentary, posing formidable qualitative and quantitative problems for various scientific and technological areas. In this work we carry out an information-theoretical analysis of the spectral energy density of a d-dimensional blackbody at temperature T by means of various entropy-like quantities (disequilibrium, Shannon entropy, Fisher information) as well as by three (dimensionless) complexity measures (Crámer-Rao, Fisher-Shannon and LMC). All these frequency-functional quantities are calculated and discussed in terms of temperature and dimensionality. It is shown that all three measures of complexity have an universal character in the sense that they depend neither on temperature nor on the Planck and Boltzmann constants, but only on the the space dimensionality d. Moreover, they decrease when d is increasing; in particular, the values 2.28415, 1.90979 and 1.17685 are found for the Crámer-Rao, Fisher-Shannon and LMC measures of complexity of the 3-dimensional blackbody radiation, respectively. In addition, beyond the frequency at which the spectral density is maximum (which follows the well-known Wien displacement law), three further characteristic frequencies are defined in terms of the previous entropy quantities; they are shown to obey Wien-like laws. The potential usefulness of these distinctive features of the blackbody spectrum is physically discussed.

Information-theoretic measures for a position-dependent mass system in an infinite potential well

“…These measures complement each other and they characterise different aspects of the distribution ρ. For comparing, the Shannon and Fisher lengths (denoted by L S and L F ) are defined [28,27]…”

Thermal Uncertainty Relations and LMC Structural Quantifiers

“…Based on a recent discussion by Nagata [1], who analyzes finite-temperature uncertainties and their relation with the LMC structural quantifiers C (statistical complexity) and D (disequilibrium) [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. We will connect them with TUR tenets.…”

“…This intermediate stage has been successfully quantified in the last 20 years by a quantity that came to be called the statistical complexity C, advanced in Ref. [11], that can be properly regarded as an structure-content quantifier [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. In [11], its authors established a kind of "distance" in probability space (PS) that they baptized the disequilibrium D. What does it measure?…”

“…In fact, C has been of utility in the realm of non complex systems (see Ref. [24,25] and references therein).…”

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

“…(normalized to unity), where Γ(x) and ζ(x) denote the Euler gamma function and the Riemann zeta function [52], respectively. This investigation will be done by means of a novel class of biparametric measures of complexity of Fisher-Rényi type which allows us to go further beyond the 2014-dated work [53] based on the entropy-like measures of ρ The structure of the work is the following. First, we define and explore the main properties of the biparametric complexities and their entropy-like components (Rényi entropy, biparametric Fisher information) of a general continuous one-dimensional probability distribution.…”