Continuity of a class of entropies and relative entropies
arXiv:math-ph/0208038
Abstract
The present paper studies continuity of generalized entropy functions and relative entropies defined using the notion of a deformed logarithmic function. In particular, two distinct definitions of relative entropy are discussed. As an application, all considered entropies are shown to satisfy Lesche's stability condition. The entropies of Tsallis' nonextensive thermostatistics are taken as examples.
Revised version, with change of title and changes in notations