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arXiv · 2103.06650

A Generalization of the Concavity of R\'{e}nyi Entropy Powe

Laigang Guo·Chun-Ming Yuan·Xiao-Shan Gao
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Abstract

Recently, Savar\'{e}-Toscani proved that the R\'{e}nyi entropy power of general probability densities solving the $p$-nonlinear heat equation in $\mathbb{R}^n$ is always a concave function of time, which extends Costa's concavity inequality for Shannon's entropy power to R\'{e}nyi entropies. In this paper, we give a generalization of Savar\'{e}-Toscani's result by giving a class of sufficient conditions of the parameters under which the concavity of the R\'{e}nyi entropy power is still valid. These conditions are quite general and include the parameter range given by Savar\'{e}-Toscani as special cases. Also, the conditions are obtained with a systematical approach.

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Laigang Guo, Chun-Ming Yuan, Xiao-Shan Gao. 2021-03-11. A Generalization of the Concavity of R\'{e}nyi Entropy Powe. https://doi.org/10.3390/e23121593

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