A generalization of Costa's Entropy Power Inequality

TL;DR

This paper generalizes Costa's Entropy Power Inequality by studying Shannon's entropy power along entropic interpolations, providing two proofs—one via $ extGamma$-calculus and another with an explicit remainder term—to deepen understanding of entropy concavity.

Contribution

It introduces a broader framework for entropy power inequalities and offers two novel proofs, one abstract and one explicit, enhancing theoretical understanding.

Findings

Generalization of Costa's Entropy Power Inequality

Two independent proofs provided: $ extGamma$-calculus and explicit remainder term

Characterization of equality cases in the generalized inequality

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 $\Gamma$-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.