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...
| Autores: | , , |
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| 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 |
| 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. |
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