Journal of Statistical Physics

, Volume 52, Issue 1–2, pp 479–487 | Cite as

Possible generalization of Boltzmann-Gibbs statistics

  • Constantino Tsallis
Short Communications

Abstract

With the use of a quantity normally scaled in multifractals, a generalized form is postulated for entropy, namelySqk [1 – ∑i=1W piq]/(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 words

Generalized statistics entropy multifractals statistical ensembles 

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References

  1. 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. 2.
    A. Rényi,Probability Theory (North-Holland, 1970).Google Scholar

Copyright information

© Plenum Publishing Corporation 1988

Authors and Affiliations

  • Constantino Tsallis
    • 1
  1. 1.Centro Brasileiro de Pesquisas Fisicas-CBPF/CNPqRio de Janeiro, RJBrazil

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