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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L^{2}$ </tex-math></inline-formula> -Wasserstein gradient flows of corresponding entropy functionals. This result extends the result of Savaré and Toscani (2014) on the concavity of Rényi entropy powers and reveals a connection to Rényi entropy power inequalities by Bobkov and Marsiglietti (2017).
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