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

TL;DR

This paper generalizes the concavity of Rényi entropy power for solutions to the p-nonlinear heat equation, providing broader conditions under which this property holds, extending prior results by Savaré-Toscani.

Contribution

It introduces a systematic approach to identify broad parameter conditions ensuring Rényi entropy power concavity, extending previous specific cases.

Findings

Established broader parameter conditions for concavity

Included previous results as special cases

Provided a systematic method for analysis

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.