The Concavity of Rényi Entropy Power

We associate to the pth Rényi entropy a definition of entropy power, which is the natural extension of Shannon's entropy power and exhibits a nice behavior along solutions to the p-nonlinear heat equation in Rn. 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 behavior in correspondence to the Barenblatt source-type solutions. This result extends Costa's concavity inequality for Shannon's entropy power to Rényi entropies.