Inserted: 23 dec 2020
Last Updated: 8 jun 2022
Journal: IEEE Transactions on Information Theory
Aim of this short note is to study Shannon's entropy power along entropic interpolations, thus generalizing Costa's concavity theorem. We shall provide two proofs of independent interest: the former by $\Gamma$-calculus, hence applicable to more abstract frameworks; the latter with an explicit remainder term, reminiscent of 20, allowing us to characterize the case of equality.