A generalization of Costa's Entropy Power Inequality

12/22/2020

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by   Luca Tamanini, et al.

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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 Γ-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.