A Strengthened Entropy Power Inequality for Log-Concave Densities
A Strengthened Entropy Power Inequality for Log-Concave Densities
We show that Shannon's entropy-power inequality admits a strengthened version in the case in which the densities are log-concave. In such a case, in fact, one can extend the Blachman-Stam argument to obtain a sharp inequality for the second derivative of Shannon's entropy functional with respect to the heat semigroup.