Gravothermal catastrophe and Tsallis’ generalized entropy of self-gravitating systems

Atsushi Taruya and Masa-aki Sakagami

Physica A: Statistical Mechanics and its Applications, 2002, vol. 307, issue 1, 185-206

Abstract: We present a first physical application of Tsallis’ generalized entropy to the thermodynamics of self-gravitating systems. The stellar system confined in a spherical cavity of radius re exhibits an instability, so-called gravothermal catastrophe, which has been originally investigated by Antonov (Vestn. Leningrad Gros. Univ. 7 (1962) 135) and Lynden-Bell and Wood (Mon. Not. R. Astron. Soc. 138 (1968) 495) on the basis of the maximum entropy principle for the phase-space distribution function. In contrast to previous analyses using the Boltzmann–Gibbs entropy, we apply the Tsallis-type generalized entropy to seek the equilibrium criteria. Then the distribution function of Vlassov–Poisson system can be reduced to the stellar polytrope system. Evaluating the second variation of Tsallis entropy and solving the zero eigenvalue problem explicitly, we find that the gravothermal instability appears in cases with polytrope index n>5. The critical point characterizing the onset of instability are obtained, which exactly matches with the results derived from the standard turning-point analysis. The results give an important suggestion that the Tsallis’ generalized entropy is indeed applicable and viable to the long-range nature of the self-gravitating system.

Keywords: Self-gravitating system; Gravothermal instability; Generalized entropy (search for similar items in EconPapers)
Date: 2002
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:307:y:2002:i:1:p:185-206

DOI: 10.1016/S0378-4371(01)00622-7

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