Modern statistical mechanics – Approaching complexity in natural, artificial and social sciences

Complexity of natural, artificial and social systems can be efficiently studied by using concepts of statistical mechanics, very especially of its modern version — nonextensive statistical mechanics — based on nonadditive entropies, which generalize the celebrated Boltzmann-Gibbs-Shannon-von Neumann entropy. A brief introduction to the physical motivations of this generalization, its connections with generalized forms of the Central Limit Theorem and of the Large Deviation Theory, and some illustrative applications in various areas of knowledge will be presented. An updated bibliography is available at tsallis.cat.cbpf.br/biblio.htm