Article

Astrophysics and Space Science

, Volume 290, Issue 3, pp 259-274

First online:

Nonextensive Statistical Mechanics: Some Links with Astronomical Phenomena

  • Constantino TsallisAffiliated withCentro Brasileiro de Pesquisas Físicas
  • , Constantino TsallisAffiliated withSanta Fe Institute Email author 
  • , Domingo PratoAffiliated withFacultad de Matematica, Astronomia y Fisica, Universidad Nacional de Cordoba
  • , Angel R. PlastinoAffiliated withFacultad de Ciencias Astronomicas y Geofisicas, Universidad Nacional de La Plata and CONICET
  • , Angel R. PlastinoAffiliated withDepartament de Fisica, Universitat de les Illes Balears

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Abstract

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 S BG=−k i p i ln p i, the nonextensive one is based on the form S q=k(1 −∑ i p i q)/(q− 1) (with S 1=S BG). 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 S q with a few constraints is equivalent to optimizing S BG with an infinite number of constraints.

nonextensive statistical mechanics Tsallis entropy solar neutrino problem cosmic rays polytropes