This article proposes a new two-parameter generalized entropy, which can be reduced to the Tsallis and the Shannon entropy for specific values of its parameters. We develop a number of information-theoretic properties of this generalized entropy and divergence, for instance, the sub-additive property, strong sub-additive property, joint convexity, and information monotonicity. This article presents an exposit investigation on the information-theoretic and information-geometric characteristics of the new generalized entropy and compare them with the properties of the Tsallis and the Shannon entropy.

翻译：本文提出了一种新的双参数广义熵，在特定参数取值下可退化为Tsallis熵和Shannon熵。我们建立了该广义熵及其散度的若干信息论特性，包括次可加性、强次可加性、联合凸性和信息单调性。本文系统阐释了新广义熵的信息论与信息几何特征，并将其与Tsallis熵及Shannon熵的性质进行了对比分析。