The concavity of generalized entropy powers

2022/02/25 by Mario Bukal, Bukal, Mario
Biochemistry, Genetics and Molecular Biology · Mathematics · #Diffusion and Search Dynamics #FOS: Computer and information sciences #Information Theory (cs.IT) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2202.12527

openalex publication_date 2022/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we introduce a new family of entropy powers which are related to generalized entropies, called Sharma-Mittal entropies, and we prove their concavity along diffusion processes generated by L²-Wasserstein gradient flows of corresponding entropy functionals. This result extends the result of Savaré and Toscani on the concavity of Rényi entropy powers (IEEE Trans. Inf. Theory, 2014) and reveals a connection to Rényi entropy power inequalities by Bobkov and Marsiglietti (IEEE Trans. Inf. Theory, 2017).

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