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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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