The concavity of generalized entropy powers

02/25/2022

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by   Mario Bukal, et al.

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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 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).