Possible generalization of Boltzmann-Gibbs statistics
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With the use of a quantity normally scaled in multifractals, a generalized form is postulated for entropy, namelyS q ≡k [1 – ∑ i=1 W p i q ]/(q-1), whereq∈ℝ characterizes the generalization andpi are the probabilities associated withW (microscopic) configurations (W∈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 theq→1 limit.
Key wordsGeneralized statistics entropy multifractals statistical ensembles
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- 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).Google Scholar
- 2.A. Rényi,Probability Theory (North-Holland, 1970).Google Scholar