A Note on the Connection between Non-Additive Entropy and <i>h</i>-Derivative

Abstract

In order to study as a whole a wide part of entropy measures, we introduce a two-parameter non-extensive entropic form with respect to the h-derivative, which generalizes the conventional Newton–Leibniz calculus. This new entropy, Sh,h′, is proved to describe the non-extensive systems and recover several types of 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.

Keywords

• non-additive entropy
• <i>h</i>-derivative
• <i>S</i>_{<i>h</i>,<i>h</i>′}-entropy