---
OA_place: repository
OA_type: green
_id: '21132'
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.
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."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Giovanni
  full_name: Brigati, Giovanni
  id: 63ff57e8-1fbb-11ee-88f2-f558ffc59cf1
  last_name: Brigati
- first_name: Francis
  full_name: Lörler, Francis
  last_name: Lörler
- first_name: Lihan
  full_name: Wang, Lihan
  last_name: Wang
citation:
  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>
  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>
  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>.
  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.
  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.
date_created: 2026-02-01T23:01:43Z
date_published: 2026-02-01T00:00:00Z
date_updated: 2026-02-16T10:02:47Z
day: '01'
department:
- _id: JaMa
doi: 10.3934/krm.2025020
ec_funded: 1
external_id:
  arxiv:
  - '2412.10890'
intvolume: '        20'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2412.10890
month: '02'
oa: 1
oa_version: Preprint
page: 34-55
project:
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
  call_identifier: H2020
  grant_number: '101034413'
  name: 'IST-BRIDGE: International postdoctoral program'
publication: Kinetic and Related Models
publication_identifier:
  eissn:
  - 1937-5077
  issn:
  - 1937-5093
publication_status: epub_ahead
publisher: American Institute of Mathematical Sciences
quality_controlled: '1'
scopus_import: '1'
status: public
title: Hypocoercivity meets lifts
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 20
year: '2026'
...