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Entropic upper bound on gravitational binding energy

Author

Listed:
  • Vignat, C.
  • Plastino, A.
  • Plastino, A.R.

Abstract

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.

Suggested Citation

  • Vignat, C. & Plastino, A. & Plastino, A.R., 2011. "Entropic upper bound on gravitational binding energy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(13), pages 2491-2496.
  • Handle: RePEc:eee:phsmap:v:390:y:2011:i:13:p:2491-2496
    DOI: 10.1016/j.physa.2011.02.042
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    Cited by:

    1. Siddiqui, Maheen & Wedemann, Roseli S. & Jensen, Henrik Jeldtoft, 2018. "Avalanches and generalized memory associativity in a network model for conscious and unconscious mental functioning," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 127-138.

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