Entropic upper bound on gravitational binding energy
We prove that the gravitational binding energy Ω of a self gravitating system described by a mass density distribution ρ(x) admits an upper bound B[ρ(x)] given by a simple function of an appropriate, non-additive Tsallis' power-law entropic functional Sq evaluated on the density ρ. The density...
| Authors: | , , |
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| Format: | article |
| Status: | Published version |
| Publication Date: | 2011 |
| Country: | Argentina |
| Institution: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repository: | CONICET Digital (CONICET) |
| Language: | English |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/95036 |
| Online Access: | http://hdl.handle.net/11336/95036 |
| Access Level: | Open access |
| Keyword: | ENTROPIC BOUND TO BINDING ENERGY GRAVITATION TSALLIS' STATISTICS https://purl.org/becyt/ford/1.3 https://purl.org/becyt/ford/1 |
| Summary: | We prove that the gravitational binding energy Ω of a self gravitating system described by a mass density distribution ρ(x) admits an upper bound B[ρ(x)] given by a simple function of an appropriate, non-additive Tsallis' power-law entropic functional Sq evaluated on the density ρ. The density distributions that saturate the entropic bound have the form of isotropic q-Gaussian distributions. These maximizer distributions correspond to the Plummer density profile, well-known in astrophysics. A heuristic scaling argument is advanced suggesting that the entropic bound B[ρ(x)] is unique, in the sense that it is unlikely that exhaustive entropic upper bounds not based on the alluded Sq entropic measure exit. The present findings provide a new link between the physics of self gravitating systems, on one hand, and the statistical formalism associated with non-additive, power-law entropic measures, on the other hand. © 2011 Elsevier B.V. All rights reserved. |
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