Generalized entropy arising from a distribution ofqindices

Abstract

It is by now well known that the Boltzmann-Gibbs (BG) entropy can be usefully generalized using the non-extensive entropies, which have been applied to a wide range of phenomena. However, it seems that even more general entropies could be useful in order to describe other complex physical systems, a task which has already been undertaken in the literature. Following this approach, we introduce here a quite general entropy based on a distribution of q indices thus generalizing S(q). We establish some general mathematical properties for the new entropic functional and explore some examples. We also exhibit a procedure for finding, given any entropic functional, the q-indices distribution that produces it. Finally, on the road to establishing a quite general statistical mechanics, we briefly address possible generalized constraints under which the present entropy could be extremized, in order to produce canonical-ensemble-like stationary-state distributions for Hamiltonian systems.