Maximum entropy approach to stretched exponential probability distributions

We introduce a nonextensive entropy functional S-eta whose optimization und er simple constraints (mean values of some standard quantities) yields stre tched exponential probability distributions, which occur in many complex sy stems. The new entropy functional is characterized by a parameter eta (the stretching exponent) such that for eta = 1 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. S-et a possesses the usual properties of positivity, equiprobability, concavity and irreversibility and verifies Khinchin axioms except the one related to additivity since S-eta is nonextensive. The entropy S-eta is shown to be su peradditive for eta < 1 and subadditive for eta > 1.