Abstract
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 <inline-formula> <tex-math notation="LaTeX">$\Gamma $ </tex-math></inline-formula>-calculus, hence applicable to more abstract frameworks; the latter with an explicit remainder term, reminiscent of Villani (IEEE Trans. Inf. Theory, 2006), allowing us to characterize the case of equality.
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