Nonadditive entropy, central limit theorem, and statistical mechanics

Professor Constantino Tsallis, Centro Brasileiro de Pesquisas F´ısicas, Rio de Janeiro presents this lecture.

Abstract: The (additive) Boltzmann-Gibbs-von Neumann-Shannon (BG) entropy is extensive in the thermodynamical sense for say classical short-rangeinteracting and other relatively standard systems. The situation is more subtle for complex systems such as quantum entangled ones, long-standing quasi stationary states in classical long-range-interacting Hamiltonian systems, opticallatices, plasma, among others. The nonadditive entropy Sq (S1 being the BG entropy) appears to be extensive for a special value of the index q which differs from unity. This class of systems is discussed,. as well as their connections to the Central Limit Theorem, which mathematically grounds BG statistical mechanics. Some applications of the theory to other areas of knowledge (edge of chaos, networks, economics, engineering) will also be briefly mentioned.

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