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Possible generalization of Boltzmann-Gibbs statistics. (English) Zbl 1082.82501
Summary: With the use of a quantity normally scaled in multifractals, a generalized form is postulated for entropy, namely $$S_q \equiv k [1 - \sum_{i =1} W _{p_i} q ]/(q-1)$$, where $$q\in \mathbb R$$ characterizes the generalization andp i are the probabilities associated with $$W$$ (microscopic) configurations ($$W \in \mathbb N$$). The main properties associated with this entropy are established, particularly those corresponding to the microcanonical and canonical ensembles. The Boltzmann-Gibbs statistics is recovered as the $$q\to 1$$ limit.

##### MSC:
 82B03 Foundations of equilibrium statistical mechanics
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##### References:
 [1] H. G. E. Hentschel and I. Procaccia,Physica D 8:435 (1983); T. C. Halsley, M. H. Jensen, L. P. Kadanoff, I. Procaccia, and B. I. Shraiman,Phys. Rev. A 33:1141 (1986); G. Paladin and A. Vulpiani,Phys. Rep. 156:147 (1987). · Zbl 0538.58026 · doi:10.1016/0167-2789(83)90235-X [2] A. Rényi,Probability Theory (North-Holland, 1970).
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