This article proposes a new two-parameter generalized entropy, which can be reduced to the Tsallis and Shannon entropies 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 Shannon entropies.

中文翻译：

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二参数熵及其基本性质

本文提出了一种新的双参数广义熵，对于其参数的特定值，可以将其简化为 Tsallis 和 Shannon 熵。我们开发了这种广义熵和散度的许多信息论性质，例如，子可加性、强子可加性、联合凸性和信息单调性。本文对新广义熵的信息理论和信息几何特征进行了阐述性研究，并将它们与 Tsallis 和 Shannon 熵的性质进行了比较。