English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We study a class of ergodic quantum Markov semigroups on finite-dimensionalunital $C^*$-algebras. These semigroups have a unique stationary state$\sigma$, and we are concerned with those that satisfy a quantum detailedbalance condition with respect to $\sigma$. We show that the evolution on theset of states that is given by such a quantum Markov semigroup is gradient flowfor the relative entropy with respect to $\sigma$ in a particular Riemannianmetric 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 uniformlyconvex with respect to the Riemannian metric introduced here. As a consequence,we obtain a number of new inequalities for the decay of relative entropy forergodic quantum Markov semigroups with detailed balance.

Gradient flow and entropy inequalities for quantum Markov semigroups with detailed balance