On the Extensivity of the EntropySq, theq-Generalized Central Limit Theorem and theq-Triplet

First, we briefly review the conditions under which the entropy $S_q$ can beextensive (Tsallis, Gell-Mann and Sato, Proc. Natl. Acad. Sc. USA (2005), inpress; cond-mat/0502274), as well as the possible $q$-generalization of thecentral limit theorem (Moyano, Tsallis and Gell-Mann, cond-mat/0509229). Then,we address the $q$-triplet recently determined in the solar wind (Burlaga andVinas, Physica A {\bf 356}, 375 (2005)) and its possible relation with thespace-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 $r$).Comment: 9 pages including 3 figures. Invited lecture at the International Conference on Complexity and Nonextensivity - New Trends in Statistical Mechanics (Yukawa Institute for Theoretical Physics, Kyoto, 14-18 March 2005). To appear in Prog. Theor. Phys. Supplement, eds. M. Sakagami, N. Suzuki and S. Ab