A note on the connection between nonextensive entropy and $h$-derivative

Abstract

In order to study as a whole the major part of entropy measures, we introduce a two-parameter non-extensive entropic form with respect to the \textit{h}-derivative which generalizes the conventional Newton-Leibniz calculus. This new entropy, $S_{h,h'}$, is proved to describe the non-extensive systems and recover several types of the well-known non-extensive entropic expressions, such as the Tsallis entropy, the Abe entropy, the Shafee entropy, the Kaniadakis entropy and even the classical Boltzmann\,--\,Gibbs one. As a generalized entropy, its corresponding properties are also analyzed.Comment: 6 pages, 1 figur