Implication of Tsallis entropy in the Thomas–Fermi model for self-gravitating fermions

Journal Article · Sat Mar 15 00:00:00 EDT 2014 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/J.AOP.2013.11.016· OSTI ID:22224298

Ourabah, Kamel; Tribeche, Mouloud

The Thomas–Fermi approach for self-gravitating fermions is revisited within the theoretical framework of the q-statistics. Starting from the q-deformation of the Fermi–Dirac distribution function, a generalized Thomas–Fermi equation is derived. It is shown that the Tsallis entropy preserves a scaling property of this equation. The q-statistical approach to Jeans’ instability in a system of self-gravitating fermions is also addressed. The dependence of the Jeans’ wavenumber (or the Jeans length) on the parameter q is traced. It is found that the q-statistics makes the Fermionic system unstable at scales shorter than the standard Jeans length. -- Highlights: •Thomas–Fermi approach for self-gravitating fermions. •A generalized Thomas–Fermi equation is derived. •Nonextensivity preserves a scaling property of this equation. •Nonextensive approach to Jeans’ instability of self-gravitating fermions. •It is found that nonextensivity makes the Fermionic system unstable at shorter scales.

• OSTI ID: 22224298
• Journal Information: Annals of Physics (New York), Vol. 342; Other Information: Copyright (c) 2013 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DISTRIBUTION FUNCTIONS
ENTROPY
EQUATIONS
FERMIONS
INSTABILITY
LENGTH
STATISTICAL MECHANICS
STATISTICS