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Biparametric complexities and generalized Planck radiation law
- Source :
- Journal of Physics A: Mathematical and Theoretical. 50:505001
- Publication Year :
- 2017
- Publisher :
- IOP Publishing, 2017.
-
Abstract
- Complexity theory embodies some of the hardest, most fundamental and most challenging open problems in modern science. The very term complexity is very elusive, so that the main goal of this theory is to find meaningful quantifiers for it. In fact we need various measures to take into account the multiple facets of this term. Here some biparametric Cr\'amer-Rao and Heisenberg-R\'enyi measures of complexity of continuous probability distributions are defined and discussed. Then, they are applied to the blackbody radiation at temperature T in a d-dimensional universe. It is found that these dimensionless quantities do not depend on T nor on any physical constants. So, they have an universal character in the sense that they only depend on the spatial dimensionality. To determine these complexity quantifiers we have calculated their dispersion (typical deviations) and entropy (R\'enyi entropies and the generalized Fisher information) constituents. They are found to have a temperature-dependent behavior similar to the celebrated Wien's displacement law of the dominant frequency $\nu_{max}$ at which the spectrum reaches its maximum. Moreover, they allow us to gain insights into new aspects of the d-dimensional blackbody spectrum and about the quantification of quantum effects associated with space dimensionality.
- Subjects :
- Statistics and Probability
Physics
Statistical Mechanics (cond-mat.stat-mech)
FOS: Physical sciences
General Physics and Astronomy
Statistical and Nonlinear Physics
Radiation
01 natural sciences
010305 fluids & plasmas
Theoretical physics
symbols.namesake
Modeling and Simulation
0103 physical sciences
symbols
Planck
010306 general physics
Condensed Matter - Statistical Mechanics
Mathematical Physics
Subjects
Details
- ISSN :
- 17518121 and 17518113
- Volume :
- 50
- Database :
- OpenAIRE
- Journal :
- Journal of Physics A: Mathematical and Theoretical
- Accession number :
- edsair.doi.dedup.....0cf091b3ff0bf3452f9b602c4e64c96d