On the problem of reversibility of the entropy power inequality

Abstract

As was shown recently by the authors, the entropy power inequality can be reversed for independent summands with sufficiently concave densities, when the distributions of the summands are put in a special position. In this note it is proved that reversibility is impossible over the whole class of convex probability distributions. Related phenomena for identically distributed summands are also discussed.

13 pages

References in corpus (3)

• Reverse Brunn-Minkowski and reverse entropy power inequalities for convex measures
• Sumset and Inverse Sumset Inequalities for Differential Entropy and Mutual Information
• Dimensional behaviour of entropy and information

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• Sharp moment-entropy inequalities and capacity bounds for log-concave distributions
• Concentration of information content for convex measures
• Volumes of subset Minkowski sums and the Lyusternik region
• Reversals of Rényi Entropy Inequalities under Log-Concavity
• Rogers-Shephard inequality for log-concave functions
• Active embedding search via noisy paired comparisons