IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v307y2002i1p185-206.html
   My bibliography  Save this article

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

Author

Listed:
  • Taruya, Atsushi
  • Sakagami, Masa-aki

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.

Suggested Citation

  • Taruya, Atsushi & Sakagami, Masa-aki, 2002. "Gravothermal catastrophe and Tsallis’ generalized entropy of self-gravitating systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 307(1), pages 185-206.
    • Handle: RePEc:eee:phsmap:v:307:y:2002:i:1:p:185-206
    DOI: 10.1016/S0378-4371(01)00622-7
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437101006227
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/S0378-4371(01)00622-7?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Xu, Zhiqiang & Rebollo-Neira, Laura & Plastino, A., 2010. "Subspace modelling for structured noise suppression," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(10), pages 2030-2035.
    2. Lima, J.A.S. & de Souza, R.E., 2005. "Power-law stellar distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 350(2), pages 303-314.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:307:y:2002:i:1:p:185-206. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.