Tsallis, Constantino Possible generalization of Boltzmann-Gibbs statistics. (English) Zbl 1082.82501 J. Stat. Phys. 52, No. 1-2, 479-487 (1988). 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. Cited in 26 ReviewsCited in 985 Documents MSC: 82B03 Foundations of equilibrium statistical mechanics Keywords:generalized statistics; entropy - multifractals; statistical ensembles PDFBibTeX XMLCite \textit{C. Tsallis}, J. Stat. Phys. 52, No. 1--2, 479--487 (1988; Zbl 1082.82501) Full Text: DOI 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 [2] A. Rényi,Probability Theory (North-Holland, 1970). This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.