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. 
Giuseppe Toscani
cs.IT math.FA math.IT