{"arxiv":1,"publication":"Kinetic and Related Models","_id":"21132","department":[{"_id":"JaMa"}],"date_created":"2026-02-01T23:01:43Z","volume":20,"oa":1,"article_type":"original","external_id":{"arxiv":["2412.10890"]},"month":"02","project":[{"grant_number":"101034413","call_identifier":"H2020","name":"IST-BRIDGE: International postdoctoral program","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c"}],"abstract":[{"lang":"eng","text":"We unify the variational hypocoercivity framework established by D. Albritton, S. Armstrong, J.-C. Mourrat, and M. Novack [2], with the notion of second-order lifts of reversible diffusion processes, recently introduced by A. Eberle and the second author [30]. We give an abstract, yet fully constructive, presentation of the theory, so that it can be applied to a large class of linear kinetic equations. As this hypocoercivity technique does not twist the reference norm, we can recover accurate and sharp convergence rates in various models. Among those, adaptive Langevin dynamics (ALD) is discussed in full detail and we show that for near-quadratic potentials, with suitable choices of parameters, it is a near-optimal second-order lift of the overdamped Langevin dynamics. As a further consequence, we observe that the Generalised Langevin Equation (GLE) is also a second-order lift, as the standard (kinetic) Langevin dynamics are, of the overdamped Langevin dynamics. Then, convergence of (GLE) cannot exceed ballistic speed, i.e. the square root of the rate of the overdamped regime. We illustrate this phenomenon with explicit computations in a benchmark Gaussian case."}],"quality_controlled":"1","status":"public","OA_type":"green","acknowledgement":"We would like to thank Andreas Eberle and Gabriel Stoltz for many helpful discussions. GB\r\nhas received funding from the European Union Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 101034413. FL wurde gefördert durch die Deutsche Forschungsgemeinschaft (DFG) im Rahmen der Exzellenzstrategie des Bundes und der Länder – GZ2047/1, Projekt-ID 390685813. LW is supported by the National Science Foundation via grant DMS-2407166. He is also indebted to the Mathematical Sciences department at Carnegie Mellon University for partly supporting his visit to Europe in July 2024. Part of this work was completed when GB and LW were visiting the Institute for Applied Mathematics in Bonn. GB and LW would like to thank IAM for their hospitality.","scopus_import":"1","citation":{"chicago":"Brigati, Giovanni, Francis Lörler, and Lihan Wang. “Hypocoercivity Meets Lifts.” <i>Kinetic and Related Models</i>. American Institute of Mathematical Sciences, 2026. <a href=\"https://doi.org/10.3934/krm.2025020\">https://doi.org/10.3934/krm.2025020</a>.","ista":"Brigati G, Lörler F, Wang L. 2026. Hypocoercivity meets lifts. Kinetic and Related Models. 20, 34–55.","mla":"Brigati, Giovanni, et al. “Hypocoercivity Meets Lifts.” <i>Kinetic and Related Models</i>, vol. 20, American Institute of Mathematical Sciences, 2026, pp. 34–55, doi:<a href=\"https://doi.org/10.3934/krm.2025020\">10.3934/krm.2025020</a>.","short":"G. Brigati, F. Lörler, L. Wang, Kinetic and Related Models 20 (2026) 34–55.","ieee":"G. Brigati, F. Lörler, and L. Wang, “Hypocoercivity meets lifts,” <i>Kinetic and Related Models</i>, vol. 20. American Institute of Mathematical Sciences, pp. 34–55, 2026.","apa":"Brigati, G., Lörler, F., &#38; Wang, L. (2026). Hypocoercivity meets lifts. <i>Kinetic and Related Models</i>. American Institute of Mathematical Sciences. <a href=\"https://doi.org/10.3934/krm.2025020\">https://doi.org/10.3934/krm.2025020</a>","ama":"Brigati G, Lörler F, Wang L. Hypocoercivity meets lifts. <i>Kinetic and Related Models</i>. 2026;20:34-55. doi:<a href=\"https://doi.org/10.3934/krm.2025020\">10.3934/krm.2025020</a>"},"date_updated":"2026-02-16T10:02:47Z","page":"34-55","ec_funded":1,"author":[{"first_name":"Giovanni","full_name":"Brigati, Giovanni","last_name":"Brigati","id":"63ff57e8-1fbb-11ee-88f2-f558ffc59cf1"},{"last_name":"Lörler","first_name":"Francis","full_name":"Lörler, Francis"},{"last_name":"Wang","first_name":"Lihan","full_name":"Wang, Lihan"}],"type":"journal_article","publication_status":"epub_ahead","OA_place":"repository","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2412.10890","open_access":"1"}],"language":[{"iso":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"American Institute of Mathematical Sciences","doi":"10.3934/krm.2025020","year":"2026","intvolume":"        20","date_published":"2026-02-01T00:00:00Z","day":"01","oa_version":"Preprint","article_processing_charge":"No","title":"Hypocoercivity meets lifts","publication_identifier":{"eissn":["1937-5077"],"issn":["1937-5093"]}}