Biparametric complexities and generalized Planck radiation law

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 the main goal of this theory is to find meaningful quantifiers for it. In fact, we need various measures to take into account the multip...

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Detalles Bibliográficos
Autores: Puertas-Centeno, D., Toranzo, I. V., Dehesa, J. S.
Tipo de recurso: artículo
Fecha de publicación:2017
País:España
Institución:Universidad Rey Juan Carlos
Repositorio:BURJC-Digital. Repositorio Institucional de la Universidad Rey Juan Carlos
OAI Identifier:oai:burjcdigital.urjc.es:10115/40183
Acceso en línea:https://hdl.handle.net/10115/40183
Access Level:acceso abierto
Palabra clave:Biparametric measures of complexity of probability distributions
Information theory of the blackbody radiation in a multidimensional universe
Planck distribution
Shannon entropy
Crámer–Rao complexity
Fisher–Shannon complexity
Heisenberg–Rényi measures of complexity
Descripción
Sumario: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 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 Crámer–Rao and Heisenberg–Rényi measures of complexity of continuous probability distributions are defined and discussed. Then, they are applied to 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 a universal character in the sense that they only depend on spatial dimensionality. To determine these complexity quantifiers, we have calculated their dispersion (typical deviations) and entropy (Rényi 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 νmax at which the spectrum reaches its maximum. Moreover, they allow us to gain insights into new aspects of the d-dimensional blackbody spectrum and the quantification of quantum effects associated with space dimensionality.