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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 k[1- i=1 W p i q]/(q-1), where q characterizes the generalization andp i are the probabilities associated with W (microscopic) configurations (W). 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 q1 limit.

82B03Foundations of equilibrium statistical mechanics
[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).