Statistical Mechanics for Complex Systems

The magnificent Boltzmann-Gibbs statistical mechanics, amalgam of first principles and theory of probabilities, constitutes one of the pillars of contemporary theoretical physics. However, it does not apply to a wide number of the so called complex systems, characterized essentially by a strong space-time entanglement of its elements. We tutorially review here the proposal for its generalization, referred to as nonextensive statistical mechanics, which emerged in 1988. It is based on nonadditive entropies (with index q ≠ 1), in contrast with the Boltzmann-Gibbs-von Neumann-Shannon entropy, which is additive (with index q = 1). Its basic foundations, as well as selected applications in physics and elsewhere, are briefly described.