Nonextensive statistical mechanics: Some links with astronomical phenomena - INSPIRE

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Nonextensive statistical mechanics: Some links with astronomical phenomena

Constantino Tsallis
(
- Rio de Janeiro, CBPF
)
,
Domingo Prato
(
- Cordoba U.
)
,
Angel R. Plastino
(
- La Plata U. and
- Balearic Islands U.
)

Jan, 2003

23 pages

Published in:

Astrophys.Space Sci. 290 (2004) 259-274

Contribution to:

11th United Nations / European Space Agency Workshop on Basic Space Science

e-Print:

cond-mat/0301590 [cond-mat]

DOI:

10.1023/B:ASTR.0000032528.99179.4f

View in:

ADS Abstract Service

reference search7 citations

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Abstract: (arXiv)

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 \sum_i p_i \ln p_i

, the nonextensive one is based on the form

S_q=k(1-\sum_ip_i^q)/(q-1)

(with

S_1=S_{BG}

). The stationary states of the former are characterized by an {\it exponential} dependence on the energy, whereas those of the latter are characterized by an (asymptotic) {\it 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 {\it 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.

References(83)

Figures(0)

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