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arXiv · 1208.1035

The concavity of Rènyi entropy power

Giuseppe Savarè·Giuseppe Toscani
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Abstract

We associate to the p-th Rényi entropy a definition of entropy power, which is the natural extension of Shannon's entropy power and exhibits a nice behaviour along solutions to the p-nonlinear heat equation in $R^n$. We show that the Rényi entropy power of general probability densities solving such equations is always a concave function of time, whereas it has a linear behaviour in correspondence to the Barenblatt source-type solutions. We then shown that the p-th Rényi entropy power of a probability density which solves the nonlinear diffusion of order p, is a concave function of time. This result extends Costa's concavity inequality for Shannon's entropy power to Rényi entropies.

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Giuseppe Savarè, Giuseppe Toscani. 2012-08-05. The concavity of Rènyi entropy power. https://doi.org/10.1109/tit.2014.2309341

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