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...

Full description

Bibliographic Details
Authors: Vignat, C., Plastino, Ángel Luis, Plastino, Ángel Ricardo
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
Description
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.