Complete gradient estimates of quantum Markov semigroups
Operator Algebras
2021-09-06 v2 Mathematical Physics
Functional Analysis
math.MP
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.
Cite
@article{arxiv.2007.13506,
title = {Complete gradient estimates of quantum Markov semigroups},
author = {Melchior Wirth and Haonan Zhang},
journal= {arXiv preprint arXiv:2007.13506},
year = {2021}
}
Comments
29 pages, some typos fixed, final version