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A Note on the Connection between Non-Additive Entropy and h-Derivative
Jin-Wen Kang1, Ke-Ming Shen1,2, Ben-Wei Zhang1
1Key Laboratory of Quark & Lepton Physics (MOE), Institute of Particle Physics, Central China Normal University, Wuhan 430079, China.
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.
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