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Possible generalization of Boltzmann-Gibbs statistics


With the use of a quantity normally scaled in multifractals, a generalized form is postulated for entropy, namelyS q k [1 – ∑ Wi=1 p qi ]/(q-1), whereq∈ℝ characterizes the generalization andp i 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.

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Tsallis, C. Possible generalization of Boltzmann-Gibbs statistics. J Stat Phys 52, 479–487 (1988).

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Key words

  • Generalized statistics
  • entropy
  • multifractals
  • statistical ensembles