Abstract
The celebrated Boltzmann-Gibbs entropy and statistical mechanics are based on hypothesis such as ergodicity and probabilistic (quasi) independence. What can be done when these simplifying hypothesis are not satisfied, which is indeed the case of many natural, artificial and social complex systems? The nonadditive entropy Sq and its associated nonextensive statistical mechanics generalize the standard Boltzmann-Gibbs theory, and provide a theoretical frame for approaching a wide class of such complex systems. Some basic concepts and some recent predictions, verifications and applications will be presented.
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