On the extensivity of the entropy Sq, the q-generalized central limit theorem and the q-triplet

Details On the extensivity of the entropy Sq, the q-generalized central limit theorem and the q-triplet On the extensivity of the entropy Sq, the q-generalized central limit theorem and the q-triplet

2005-10-05

arxiv.org/abs/cond-mat/0510125v1

Physics

Condensed Matter

Statistical Mechanics

9 pages including 3 figures. Invited lecture at the International Conference on Complexity and Nonextensivity - New Trends in

Scientific paper

10.1143/PTPS.162.1

First, we briefly review the conditions under which the entropy $S_q$ can be extensive (Tsallis, Gell-Mann and Sato, Proc. Natl. Acad. Sc. USA (2005), in press; cond-mat/0502274), as well as the possible $q$-generalization of the central limit theorem (Moyano, Tsallis and Gell-Mann, cond-mat/0509229). Then, we address the $q$-triplet recently determined in the solar wind (Burlaga and Vinas, Physica A {\bf 356}, 375 (2005)) and its possible relation with the space-dimension $d$ and with the range of the interactions (characterized by $\alpha$, the attractive potential energy being assumed to decay as $r^{-\alpha}$ at long distances $r$).

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