We prove that the reciprocal of Fisher information of a log-concave
probability density X in Rn is concave in t with respect to the
addition of a Gaussian noise Zt​=N(0,tIn​). As a byproduct of this result
we show that the third derivative of the entropy power of a log-concave
probability density X in Rn is nonnegative in t with respect to
the addition of a Gaussian noise Zt​. For log-concave densities this improves
the well-known Costa's concavity property of the entropy power