Possible generalization of Boltzmann-Gibbs statistics

Abstract

With the use of a quantity normally scaled in multifractals, a generalized form is postulated for entropy, namely Sq ≡k [1 - ∑i=1W piq]/(q-1), where q∈ℝ characterizes the generalization and pi are the probabilities associated with W (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 the q→1 limit. © 1988 Plenum Publishing Corporation.