Astrophysics and Space Science

, Volume 290, Issue 3–4, pp 259–274

Nonextensive Statistical Mechanics: Some Links with Astronomical Phenomena

  • Constantino Tsallis
  • Constantino Tsallis
  • Domingo Prato
  • Angel R. Plastino
  • Angel R. Plastino


A variety of astronomical phenomena appear to not satisfy the ergodic hypothesis in the relevant stationary state, if any. As such, there is no reason for expecting the applicability of Boltzmann–Gibbs (BG) statistical mechanics. Some of these phenomena appear to follow, instead, nonextensive statistical mechanics. In the same manner that the BG formalism is based on the entropy SBG=−kipi ln pi, the nonextensive one is based on the form Sq=k(1 −∑ipiq)/(q− 1) (with S1=SBG). The stationary states of the former are characterized by an exponential dependence on the energy, whereas those of the latter are characterized by an (asymptotic) power law. A brief review of this theory is given here, as well as of some of its applications, such as the solar neutrino problem, polytropic self-gravitating systems, galactic peculiar velocities, cosmic rays and some cosmological aspects. In addition to these, an analogy with the Keplerian elliptic orbits versus the Ptolemaic epicycles is developed, where we show that optimizing Sq with a few constraints is equivalent to optimizing SBG with an infinite number of constraints.

nonextensive statistical mechanics Tsallis entropy solar neutrino problem cosmic rays polytropes 


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Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Constantino Tsallis
    • 1
  • Constantino Tsallis
    • 2
  • Domingo Prato
    • 3
  • Angel R. Plastino
    • 4
  • Angel R. Plastino
    • 5
  1. 1.Centro Brasileiro de Pesquisas FísicasBrazil
  2. 2.Santa Fe InstituteUSA
  3. 3.Facultad de Matematica, Astronomia y FisicaUniversidad Nacional de CordobaArgentina
  4. 4.Facultad de Ciencias Astronomicas y GeofisicasUniversidad Nacional de La Plata and CONICETArgentina
  5. 5.Departament de FisicaUniversitat de les Illes BalearsPalma de MallorcaSpain

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