Skip to main content
SpringerLink
Log in

Hydrostatic equilibrium and Tsallis’ equilibrium for self-gravitating systems

  • Published:
Central European Journal of Physics

Abstract

Self-gravitating systems are generally thought to behavior non-extensively due to the long-range nature of gravitational forces. We discuss a relation between the nonextensive parameter q of Tsallis statistics, the temperature gradient and the gravitational potential based on the equation of hydrostatic equilibrium for self-gravitating systems. It is suggested that the nonextensive parameter in Tsallis statistics has a clear physical meaning with regard to the non-isothermal nature of the systems with long-range interactions. Tsallis’ equilibrium distribution for the self-gravitating systems describes the property of hydrostatic equilibrium of the systems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. S. Chandrasekhar: An introduction to the theory of stellar structure, Dover, New York, 1942; J. Binney and S. Tremaine: Galactic dynamics, Princeton University Press, Princeton, 1987.

    Google Scholar 

  2. S. Chapman and T.G. Cowling: The Mathematical Theory of Nonuniform Gases, 3rd ed., Cambridge University Press, 1970; Wang Zhuxi: An Introduction to Statistical Phhsics, The People’s Education Press, Beijing, 1965.

  3. S. Abe and A.K. Rajagopal: “Revisiting disorder and Tsallis statistics”, Science, Vol. 300, (2003), pp. 249–250; A. Plastino: “Revisiting disorder and Tsallis statistics”, Science, Vol.300, (2003), pp. 250–250; V. Latora, A. Rapisarda and A. Robledo: “Revistiting disorder and Tsallis statistics”, Science, Vol. 300, (2003), pp. 250–251.

    Article  Google Scholar 

  4. C. Tsallis: “Possible generalization of Boltzmann-Gibbs statistics”, J. Stat. Phys., Vol. 52, (1988), pp. 479–487.

    Article  MATH  MathSciNet  Google Scholar 

  5. C. Tsallis and D. Prato: “Nonextensive statistical mechanics: Some links with astronomical phenomena”, In: H.J. Haubold (Ed.): Proceedings of the Xith United Nationa/European Space Agency Workshop on Basic Space Sciences; Cordoba, 9–13 Sept. 2002, Office for Outer Space affairs/United Nations, Kluwer. Academic Publishers, Dordrecht, 2003.

    Google Scholar 

  6. J.A.S. Lima, R. Silva and J. Santos: “Jeans’ gravitational instability and nonextensive kinetic theory”, Astron. Astrophys., Vol. 396, (2002), pp. 309–313.

    Article  MATH  ADS  Google Scholar 

  7. J.L. Du: “Jeans criterion and nonextensive velocity distribution function in kinetic theory”, Phys. Lett. A, Vol. 320, (2004), pp. 347–351.

    Article  MathSciNet  Google Scholar 

  8. J.L. Du: “Jeans criterion in nonextensive statistical mechanics”, Physica A, Vol. 335, (2004), pp. 107–114.

    Article  MathSciNet  Google Scholar 

  9. A. Taruya and M. Sakagami: “Gravothermal catastrophe and Tsallis’ generalized entropy of self-gravitating systems”, Physica A, Vol. 307, (2002), pp. 185–206; M. Sakagami and A. Taruya: “Description of quasi-equilibrium states of self-gravitating systems based on nonextensive thermostatistics”, Physica A, Vol. 340, (2004), pp. 444–452.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  10. A. Plastino and A.R. Plastino: “Stellar polytropes and Tsallis’ entropy”, Phys. Lett. A, Vol. 174, (1993), pp. 384–386.

    Article  MathSciNet  ADS  Google Scholar 

  11. R. Silva and J.S. Alcaniz: “Nonextensive statistics and the stellar polytrope index”, Physica A, Vol. 341, (2004), pp. 208–211.

    Article  MathSciNet  ADS  Google Scholar 

  12. C.A. Wuensche, A.L.B. Ribeiro, F.M. Ramos and R.R. Rosa: “Nonextensivity and galaxy clustering in the universe”, Physica A, Vol. 334, (2004), pp. 743–749.

    Article  ADS  Google Scholar 

  13. A. Taruya and M. Sakagami: “Long-term evolution of stellar self-gravitating systems away from thermal equilibrium: connection with nonextensive statistics”, Phys. Rev. Lett., Vol. 90, (2003), pp. 181101.

    Article  ADS  Google Scholar 

  14. A. Taruya and M. Sakagami: “Fokker-Planck study of stellsr self-gravitating system away from the thermal equilibrium: connection with nonextensive statistics”, Physica A, Vol. 340, (2004), pp. 453–458.

    Article  MathSciNet  ADS  Google Scholar 

  15. S.H. Hansen, D. Egli, L. Hollenstein and C. Salzmann: “Dark matter distribution function from nonextensive statistical mechanics”, astro-ph/0407111.

  16. S. Abe: “Thermodynamic limit of a classical gas in nonextensive statistical mechanics: negative specific heat and polytropism”, Phys. Lett. A, Vol. 263, (1999), pp. 424–429.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  17. R. Silva and J.S. Alcaniz: “Negative heat capacity and nonextensive kinetic theory”, Phys. Lett. A, Vol. 313, (2003), pp. 393–396.

    Article  MATH  MathSciNet  Google Scholar 

  18. G. Kaniadakis, A. Lavagno and P. Quarati: “Generalized statistics and solar neutrinos”, Phys. Lett. B, Vol. 369, (1996), pp. 308–312; A. Lavagno and P. Quarati: “Classical and quantum nonextensive statistics effects in nuclear many-body problems”, Chaos, Solitons and Fractals, Vol. 13, (2002), pp. 569–580.

    Article  ADS  Google Scholar 

  19. M. Coraddu, M. Lissia, G. Mezzorani and P. Quarati: “Super-Kamiokande hep neutrino best fit: a possible signal of non-Maxwellian solar plasma”, Physica A, Vol. 326, (2003), pp. 473–481.

    Article  ADS  Google Scholar 

  20. J.A.S. Lima, R. Silva and A.R. Plastino: “Nonextensive thermostatistics and the H theorem”, Phys. Rev. Lett., Vol. 86, (2001), pp. 2938–2941.

    Article  ADS  Google Scholar 

  21. J.L. Du: “The nonextensive parameter and Tsallis distribution for self-gravitating systems”, Europhys. Lett., Vol. 67, (2004), pp. 893–899.

    Article  Google Scholar 

  22. J.L. Du: “Nonextensivity in nonequilibrium plasma systems with Coulombian longrange interactions”, Phys. Lett. A, Vol. 329, (2004), pp. 262–267.

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, School of Science, Tianjin University, 300072, Tianjin, China

    Jiulin Du

Authors
  1. Jiulin Du
    View author publications

    You can also search for this author in PubMed Google Scholar

About this article

Cite this article

Du, J. Hydrostatic equilibrium and Tsallis’ equilibrium for self-gravitating systems. centr.eur.j.phys. 3, 376–381 (2005). https://doi.org/10.2478/BF02475644

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.2478/BF02475644

Keywords

PACS (2000)

Search

Navigation