--- _id: '956' abstract: - lang: eng text: We study a class of ergodic quantum Markov semigroups on finite-dimensional unital C⁎-algebras. These semigroups have a unique stationary state σ, and we are concerned with those that satisfy a quantum detailed balance condition with respect to σ. 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 σ 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. article_processing_charge: No author: - first_name: Eric full_name: Carlen, Eric last_name: Carlen - first_name: Jan full_name: Maas, Jan id: 4C5696CE-F248-11E8-B48F-1D18A9856A87 last_name: Maas orcid: 0000-0002-0845-1338 citation: ama: Carlen E, Maas J. Gradient flow and entropy inequalities for quantum Markov semigroups with detailed balance. Journal of Functional Analysis. 2017;273(5):1810-1869. doi:10.1016/j.jfa.2017.05.003 apa: Carlen, E., & Maas, J. (2017). Gradient flow and entropy inequalities for quantum Markov semigroups with detailed balance. Journal of Functional Analysis. Academic Press. https://doi.org/10.1016/j.jfa.2017.05.003 chicago: Carlen, Eric, and Jan Maas. “Gradient Flow and Entropy Inequalities for Quantum Markov Semigroups with Detailed Balance.” Journal of Functional Analysis. Academic Press, 2017. https://doi.org/10.1016/j.jfa.2017.05.003. ieee: E. Carlen and J. Maas, “Gradient flow and entropy inequalities for quantum Markov semigroups with detailed balance,” Journal of Functional Analysis, vol. 273, no. 5. Academic Press, pp. 1810–1869, 2017. ista: Carlen E, Maas J. 2017. Gradient flow and entropy inequalities for quantum Markov semigroups with detailed balance. Journal of Functional Analysis. 273(5), 1810–1869. mla: Carlen, Eric, and Jan Maas. “Gradient Flow and Entropy Inequalities for Quantum Markov Semigroups with Detailed Balance.” Journal of Functional Analysis, vol. 273, no. 5, Academic Press, 2017, pp. 1810–69, doi:10.1016/j.jfa.2017.05.003. short: E. Carlen, J. Maas, Journal of Functional Analysis 273 (2017) 1810–1869. date_created: 2018-12-11T11:49:24Z date_published: 2017-09-01T00:00:00Z date_updated: 2023-09-22T10:00:18Z day: '01' department: - _id: JaMa doi: 10.1016/j.jfa.2017.05.003 external_id: isi: - '000406082300005' intvolume: ' 273' isi: 1 issue: '5' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1609.01254 month: '09' oa: 1 oa_version: Submitted Version page: 1810 - 1869 publication: Journal of Functional Analysis publication_identifier: issn: - '00221236' publication_status: published publisher: Academic Press publist_id: '6452' quality_controlled: '1' scopus_import: '1' status: public title: Gradient flow and entropy inequalities for quantum Markov semigroups with detailed balance type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 273 year: '2017' ...