Relative entropy has been a useful information measure in estimating the mixing/thermalization time of Markovian open quantum systems. In this talk, I will talk about some recent progresses on deriving entropy decay via a notion of coarse Ricci curvature. The idea is inspired from the recent work by Caputo, Münch, and Salez for classical Markov chains. We extend it to the quantum case based on the notion of quantum coarse Ricci curvature introduced by Gao and Rouz\'e.
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