Introduction to Nonextensive Statistical Mechanics and Thermodynamics *

In this lecture we briefly review the definition, consequences and applications of an entropy, Sq, which generalizes the usual Boltzmann-Gibbs entropy SBG (S1 = SBG), basis of the usual statistical mechanics, well known to be applicable whenever ergodicity is satisfied at the microscopic dynamical level. Such entropy Sq is based on the notion of q-exponential and presents properties not shared by other available alternative generalizations of SBG. The thermodynamics proposed in this way is generically nonextensive in a sense that will be qualified. The present framework seems to describe quite well a vast class of natural and artificial systems which are not ergodic nor close to it. The a priori calculation of q is necessary to complete the theory and we present some models where this has already been achieved. To appear in the Proceedings of the 1953-2003 Jubilee “Enrico Fermi” International Summer School of Physics The Physics of Complex Systems: New Advances & Perspectives, Directors F. Mallamace and H.E. Stanley (1-11 July 2003, Varenna sul lago di Como). The present manuscript reports the content of the lecture delivered by C. Tsallis, and is based on the corresponding notes prepared by F. Baldovin, R. Cerbino and P. Pierobon, students at the School. [email protected], [email protected], [email protected], [email protected]