The concavity of generalized entropy powers
Information Theory
2022-02-28 v1 math.IT
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 -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).
Keywords
Cite
@article{arxiv.2202.12527,
title = {The concavity of generalized entropy powers},
author = {Mario Bukal},
journal= {arXiv preprint arXiv:2202.12527},
year = {2022}
}