A note on the connection between nonextensive entropy and \textit{h}-derivative

Jin-Wen Kang, Keming Shen, Ben-Wei Zhang

Published 2019-05-19Version 1

With \textit{h}-derivative which generalizes the conventional Newton-Leibniz calculus, a general two-parameter non-extensive entropy $S_{h,h'}$ is introduced. It is found that $S_{h,h'}$ recovers, as particular cases, several types of non-extensive entropy expressions such as Tsallis entropy, Abe entropy, Shafee entropy, Kaniadakis entropy as well as the Boltzmann-Gibbs one. The corresponding properties of $S_{h,h'}$ are also analyzed.