The concavity of R\`enyi entropy power
Information Theory
2014-09-16 v1 Functional Analysis
math.IT
Abstract
We associate to the p-th R\'enyi 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 . We show that the R\'enyi 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 R\'enyi 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 R\'enyi entropies.
Keywords
Cite
@article{arxiv.1208.1035,
title = {The concavity of R\`enyi entropy power},
author = {Giuseppe Savarè and Giuseppe Toscani},
journal= {arXiv preprint arXiv:1208.1035},
year = {2014}
}