Rényi and Tsallis entropies for incomplete or overcomplete systems of events

In this article, Shannon, Rényi and Tsallis entropies are considered for a system of events characterized by an arbitrary probability distribution PP that can be incomplete, complete or overcomplete. After a suitable transformation that leads to the escort probabilities of PP, these can be written as the canonical probability distribution for a set of pseudo-energies (Hartley information, En=−lnPnEn=−lnPn) and a dimensionless parameter qq that plays the role of thermodynamics ββ. Several relations between the entropies are presented, including the analysis of compound systems. The method is illustrated with an example.