Possible generalization of Boltzmann-Gibbs statistics

Abstract

With the use of a quantity normally scaled in multifractals, a generalized form is postulated for entropy, namelyS _q ≡k [1 – ∑ ^W_i=1 p ^q_i ]/(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.