{"quality_controlled":0,"date_published":"2011-03-04T00:00:00Z","year":"2011","day":"04","abstract":[{"lang":"eng","text":"Let K be an irreducible and reversible Markov kernel on a finite set X. We construct a metric W on the set of probability measures on X and show that with respect to this metric, the law of the continuous time Markov chain evolves as the gradient flow of the entropy. This result is a discrete counterpart of the Wasserstein gradient flow interpretation of the heat flow in Rn by Jordan, Kinderlehrer and Otto (1998). The metric W is similar to, but different from, the L2-Wasserstein metric, and is defined via a discrete variant of the Benamou–Brenier formula.\n"}],"status":"public","date_created":"2018-12-11T11:55:51Z","intvolume":"       261","publication":"Journal of Functional Analysis","date_updated":"2021-01-12T06:55:28Z","main_file_link":[{"url":"http://arxiv.org/abs/1102.5238","open_access":"1"}],"page":"2250 - 2292","extern":1,"author":[{"first_name":"Jan","orcid":"0000-0002-0845-1338","full_name":"Jan Maas","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","last_name":"Maas"}],"publist_id":"4909","acknowledgement":"Supported by Rubicon subsidy 680-50-0901 of the Netherlands Organisation for Scientific Research (NWO)","publication_status":"published","volume":261,"publisher":"Academic Press","oa":1,"type":"journal_article","citation":{"apa":"Maas, J. (2011). Gradient flows of the entropy for finite Markov chains. <i>Journal of Functional Analysis</i>. Academic Press. <a href=\"https://doi.org/10.1016/j.jfa.2011.06.009 \">https://doi.org/10.1016/j.jfa.2011.06.009 </a>","short":"J. Maas, Journal of Functional Analysis 261 (2011) 2250–2292.","chicago":"Maas, Jan. “Gradient Flows of the Entropy for Finite Markov Chains.” <i>Journal of Functional Analysis</i>. Academic Press, 2011. <a href=\"https://doi.org/10.1016/j.jfa.2011.06.009 \">https://doi.org/10.1016/j.jfa.2011.06.009 </a>.","mla":"Maas, Jan. “Gradient Flows of the Entropy for Finite Markov Chains.” <i>Journal of Functional Analysis</i>, vol. 261, no. 8, Academic Press, 2011, pp. 2250–92, doi:<a href=\"https://doi.org/10.1016/j.jfa.2011.06.009 \">10.1016/j.jfa.2011.06.009 </a>.","ieee":"J. Maas, “Gradient flows of the entropy for finite Markov chains,” <i>Journal of Functional Analysis</i>, vol. 261, no. 8. Academic Press, pp. 2250–2292, 2011.","ama":"Maas J. Gradient flows of the entropy for finite Markov chains. <i>Journal of Functional Analysis</i>. 2011;261(8):2250-2292. doi:<a href=\"https://doi.org/10.1016/j.jfa.2011.06.009 \">10.1016/j.jfa.2011.06.009 </a>","ista":"Maas J. 2011. Gradient flows of the entropy for finite Markov chains. Journal of Functional Analysis. 261(8), 2250–2292."},"title":"Gradient flows of the entropy for finite Markov chains","month":"03","issue":"8","_id":"2126","doi":"10.1016/j.jfa.2011.06.009 "}