67 research outputs found
Entropy and complexity properties of the d-dimensional blackbody radiation
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, pos- ing
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 (Cr\'amer-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
Cr\'amer-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.Comment: 10 pages, 2 figure
Entropic functionals of Laguerre and Gegenbauer polynomials with large parameters
The determination of the physical entropies (R\'enyi, Shannon, Tsallis) of
high-dimensional quantum systems subject to a central potential requires the
knowledge of the asymptotics of some power and logarithmic integral functionals
of the hypergeometric orthogonal polynomials which control the wavefunctions of
the stationary states. For the -dimensional hydrogenic and oscillator-like
systems, the wavefunctions of the corresponding bound states are controlled by
the Laguerre () and Gegenbauer
() polynomials in both position and momentum
spaces, where the parameter linearly depends on . In this work we
study the asymptotic behavior as of the associated
entropy-like integral functionals of these two families of hypergeometric
polynomials
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