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• W2517591994 abstract "We study a class of ergodic quantum Markov semigroups on finite-dimensional unital $C^*$-algebras. These semigroups have a unique stationary state $sigma$, and we are concerned with those that satisfy a quantum detailed balance condition with respect to $sigma$. We show that the evolution on the set of states that is given by such a quantum Markov semigroup is gradient flow for the relative entropy with respect to $sigma$ in a particular Riemannian metric on the set of states. This metric is a non-commutative analog of the $2$-Wasserstein metric, and in several interesting cases we are able to show, in analogy with work of Otto on gradient flows with respect to the classical $2$-Wasserstein metric, that the relative entropy is strictly and uniformly convex with respect to the Riemannian metric introduced here. As a consequence, we obtain a number of new inequalities for the decay of relative entropy for ergodic quantum Markov semigroups with detailed balance." @default.
• W2517591994 created "2016-09-16" @default.
• W2517591994 creator A5045254679 @default.
• W2517591994 creator A5077320234 @default.
• W2517591994 date "2016-09-05" @default.
• W2517591994 modified "2023-09-27" @default.
• W2517591994 title "Gradient flow and entropy inequalities for quantum Markov semigroups with detailed balance" @default.
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