Boltzmann-Gibbs (BG) statistical mechanics, ergodicity, and quick mixing in phase space are intimately linked. A large variety of natural and artificial systems exist that do not fit correctly within. An important part of them appears to be adequately tractable within nonextensive statistical mechanics, a current generalization of the BG theory. A brief introduction to and the present status of the theory will be given, with special emphasis on its dynamical foundations.
Bibliography:
(i) M. Gell-Mann and C. Tsallis, "Nonextensive Entropy - Interdisciplinary Applications" (Oxford University Press, New York, 2004);
(ii) http://tsallis.cat.cbpf.br/biblio.htm