The concavity of generalized entropy powers

Mario Bukal

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arXiv · 2202.12527

The concavity of generalized entropy powers

Mario Bukal

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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 $L^2$-Wasserstein gradient flows of corresponding entropy functionals. This result extends the result of Savar\'e and Toscani on the concavity of R\'enyi entropy powers (IEEE Trans. Inf. Theory, 2014) and reveals a connection to R\'enyi entropy power inequalities by Bobkov and Marsiglietti (IEEE Trans. Inf. Theory, 2017).

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Mario Bukal. 2022-02-25. The concavity of generalized entropy powers. https://arxiv.org/abs/2202.12527

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