Maximum entropy approach to stretched exponential probability distributions

Abstract

We introduce a nonextensive entropy functional whose optimization under simple constraints (mean values of some standard quantities) yields stretched exponential probability distributions, which occur in many complex systems. The new entropy functional is characterized by a parameter (the stretching exponent) such that for the standard logarithmic entropy is recovered. We study its mathematical properties, showing that the basic requirements for a well-behaved entropy functional are verified, i.e. possesses the usual properties of positivity, equiprobability, concavity and irreversibility and verifies Khinchin axioms except the one related to additivity since is nonextensive. The entropy is shown to be superadditive for and subadditive for .