{"page":"1810 - 1869","month":"09","date_updated":"2023-09-22T10:00:18Z","volume":273,"date_created":"2018-12-11T11:49:24Z","department":[{"_id":"JaMa"}],"title":"Gradient flow and entropy inequalities for quantum Markov semigroups with detailed balance","_id":"956","author":[{"last_name":"Carlen","full_name":"Carlen, Eric","first_name":"Eric"},{"orcid":"0000-0002-0845-1338","last_name":"Maas","full_name":"Maas, Jan","first_name":"Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87"}],"year":"2017","type":"journal_article","publication_status":"published","oa_version":"Submitted Version","oa":1,"isi":1,"intvolume":"       273","publication":"Journal of Functional Analysis","external_id":{"isi":["000406082300005"]},"quality_controlled":"1","main_file_link":[{"url":"https://arxiv.org/abs/1609.01254","open_access":"1"}],"date_published":"2017-09-01T00:00:00Z","publication_identifier":{"issn":["00221236"]},"day":"01","status":"public","citation":{"short":"E. Carlen, J. Maas, Journal of Functional Analysis 273 (2017) 1810–1869.","apa":"Carlen, E., &#38; Maas, J. (2017). Gradient flow and entropy inequalities for quantum Markov semigroups with detailed balance. <i>Journal of Functional Analysis</i>. Academic Press. <a href=\"https://doi.org/10.1016/j.jfa.2017.05.003\">https://doi.org/10.1016/j.jfa.2017.05.003</a>","mla":"Carlen, Eric, and Jan Maas. “Gradient Flow and Entropy Inequalities for Quantum Markov Semigroups with Detailed Balance.” <i>Journal of Functional Analysis</i>, vol. 273, no. 5, Academic Press, 2017, pp. 1810–69, doi:<a href=\"https://doi.org/10.1016/j.jfa.2017.05.003\">10.1016/j.jfa.2017.05.003</a>.","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.","ieee":"E. Carlen and J. Maas, “Gradient flow and entropy inequalities for quantum Markov semigroups with detailed balance,” <i>Journal of Functional Analysis</i>, vol. 273, no. 5. Academic Press, pp. 1810–1869, 2017.","ama":"Carlen E, Maas J. Gradient flow and entropy inequalities for quantum Markov semigroups with detailed balance. <i>Journal of Functional Analysis</i>. 2017;273(5):1810-1869. doi:<a href=\"https://doi.org/10.1016/j.jfa.2017.05.003\">10.1016/j.jfa.2017.05.003</a>","chicago":"Carlen, Eric, and Jan Maas. “Gradient Flow and Entropy Inequalities for Quantum Markov Semigroups with Detailed Balance.” <i>Journal of Functional Analysis</i>. Academic Press, 2017. <a href=\"https://doi.org/10.1016/j.jfa.2017.05.003\">https://doi.org/10.1016/j.jfa.2017.05.003</a>."},"doi":"10.1016/j.jfa.2017.05.003","scopus_import":"1","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","article_processing_charge":"No","issue":"5","language":[{"iso":"eng"}],"publist_id":"6452","publisher":"Academic Press","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."}]}