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arXiv · 2007.13506

Complete gradient estimates of quantum Markov semigroups

Melchior Wirth·Haonan Zhang
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Abstract

In this article we introduce a complete gradient estimate for symmetric quantum Markov semigroups on von Neumann algebras equipped with a normal faithful tracial state, which implies semi-convexity of the entropy with respect to the recently introduced noncommutative 2-Wasserstein distance. We show that this complete gradient estimate is stable under tensor products and free products and establish its validity for a number of examples. As an application we prove a complete modified logarithmic Sobolev inequality with optimal constant for Poisson-type semigroups on free group factors.

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BibTeXRIS

Melchior Wirth, Haonan Zhang. 2020-07-27. Complete gradient estimates of quantum Markov semigroups. https://doi.org/10.1007/s00220-021-04199-4

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