<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of hal-00495517</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-05-09T04:26:55+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Langevin dynamics with constraints and computation of free energy differences</title>
            <author role="aut">
              <persName>
                <forename type="first">Tony</forename>
                <surname>Lelièvre</surname>
              </persName>
              <email type="md5">bc72b1e21a055812f8d5a7b045f2c19f</email>
              <email type="domain">enpc.fr</email>
              <ptr type="url" target="http://cermics.enpc.fr/~lelievre/"/>
              <idno type="idhal" notation="string">tony-lelievre</idno>
              <idno type="idhal" notation="numeric">170972</idno>
              <idno type="halauthorid" notation="string">5968-170972</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-3412-113X</idno>
              <idno type="GOOGLE SCHOLAR">https://scholar.google.fr/citations?user=aKjdYBwAAAAJ&amp;hl=fr</idno>
              <idno type="IDREF">https://www.idref.fr/111632021</idno>
              <orgName ref="#struct-301545"/>
              <affiliation ref="#struct-51621"/>
              <affiliation ref="#struct-2429"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Mathias</forename>
                <surname>Rousset</surname>
              </persName>
              <email type="md5">0c0a37dad0cbbec758e2f22686a78759</email>
              <email type="domain">inria.fr</email>
              <idno type="idhal" notation="string">mathias-rousset</idno>
              <idno type="idhal" notation="numeric">736245</idno>
              <idno type="halauthorid" notation="string">559-736245</idno>
              <idno type="ORCID">https://orcid.org/0000-0001-6232-0702</idno>
              <affiliation ref="#struct-56018"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Gabriel</forename>
                <surname>Stoltz</surname>
              </persName>
              <email type="md5">071a553aa51905c9b9a5e8e383603a1b</email>
              <email type="domain">enpc.fr</email>
              <idno type="idhal" notation="numeric">830389</idno>
              <idno type="halauthorid" notation="string">110551-830389</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-2797-5938</idno>
              <idno type="IDREF">https://www.idref.fr/131148133</idno>
              <orgName ref="#struct-301545"/>
              <affiliation ref="#struct-51621"/>
              <affiliation ref="#struct-2429"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Gabriel</forename>
                <surname>Stoltz</surname>
              </persName>
              <email type="md5">6c3787e088b847e4c680ad1f4689bb38</email>
              <email type="domain">cermics.enpc.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2010-06-28 09:36:06</date>
              <date type="whenWritten">2010-06-25</date>
              <date type="whenModified">2026-01-28 15:12:03</date>
              <date type="whenReleased">2010-06-28 09:36:06</date>
              <date type="whenProduced">2010-06-25</date>
              <ref type="externalLink" target="http://arxiv.org/pdf/1006.4914"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="115915">
                <persName>
                  <forename>Gabriel</forename>
                  <surname>Stoltz</surname>
                </persName>
                <email type="md5">6c3787e088b847e4c680ad1f4689bb38</email>
                <email type="domain">cermics.enpc.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-00495517</idno>
            <idno type="halUri">https://hal.science/hal-00495517</idno>
            <idno type="halBibtex">lelievre:hal-00495517</idno>
            <idno type="halRefHtml">2010</idno>
            <idno type="halRef">2010</idno>
            <availability status="restricted"/>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="ENPC" corresp="PARISTECH">École nationale des ponts et chaussées </idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="INRIA">INRIA - Institut National de Recherche en Informatique et en Automatique</idno>
            <idno type="stamp" n="INRIA-ROCQ">INRIA Paris - Rocquencourt</idno>
            <idno type="stamp" n="CERMICS" corresp="ENPC">Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique</idno>
            <idno type="stamp" n="INRIA-LILLE">INRIA Lille - Nord Europe</idno>
            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
            <idno type="stamp" n="PARISTECH">ParisTech</idno>
            <idno type="stamp" n="INRIA_TEST">INRIA - Institut National de Recherche en Informatique et en Automatique</idno>
            <idno type="stamp" n="PREPRINT">Preprint HAL Ecole des Ponts ParisTech</idno>
            <idno type="stamp" n="TESTALAIN1">TESTALAIN1</idno>
            <idno type="stamp" n="INRIA2">INRIA 2</idno>
            <idno type="stamp" n="UNIV-LILLE">Université de Lille</idno>
            <idno type="stamp" n="LPP-MATH">Laboratoire Paul Painlevé (UMR8524)</idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="1">Not set</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Langevin dynamics with constraints and computation of free energy differences</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Tony</forename>
                    <surname>Lelièvre</surname>
                  </persName>
                  <email type="md5">bc72b1e21a055812f8d5a7b045f2c19f</email>
                  <email type="domain">enpc.fr</email>
                  <ptr type="url" target="http://cermics.enpc.fr/~lelievre/"/>
                  <idno type="idhal" notation="string">tony-lelievre</idno>
                  <idno type="idhal" notation="numeric">170972</idno>
                  <idno type="halauthorid" notation="string">5968-170972</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-3412-113X</idno>
                  <idno type="GOOGLE SCHOLAR">https://scholar.google.fr/citations?user=aKjdYBwAAAAJ&amp;hl=fr</idno>
                  <idno type="IDREF">https://www.idref.fr/111632021</idno>
                  <orgName ref="#struct-301545"/>
                  <affiliation ref="#struct-51621"/>
                  <affiliation ref="#struct-2429"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Mathias</forename>
                    <surname>Rousset</surname>
                  </persName>
                  <email type="md5">0c0a37dad0cbbec758e2f22686a78759</email>
                  <email type="domain">inria.fr</email>
                  <idno type="idhal" notation="string">mathias-rousset</idno>
                  <idno type="idhal" notation="numeric">736245</idno>
                  <idno type="halauthorid" notation="string">559-736245</idno>
                  <idno type="ORCID">https://orcid.org/0000-0001-6232-0702</idno>
                  <affiliation ref="#struct-56018"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Gabriel</forename>
                    <surname>Stoltz</surname>
                  </persName>
                  <email type="md5">071a553aa51905c9b9a5e8e383603a1b</email>
                  <email type="domain">enpc.fr</email>
                  <idno type="idhal" notation="numeric">830389</idno>
                  <idno type="halauthorid" notation="string">110551-830389</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-2797-5938</idno>
                  <idno type="IDREF">https://www.idref.fr/131148133</idno>
                  <orgName ref="#struct-301545"/>
                  <affiliation ref="#struct-51621"/>
                  <affiliation ref="#struct-2429"/>
                </author>
              </analytic>
              <monogr>
                <imprint/>
              </monogr>
              <idno type="arxiv">1006.4914</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <classCode scheme="halDomain" n="phys.cond.cm-sm">Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech]</classCode>
              <classCode scheme="halTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
              <classCode scheme="halOldTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
              <classCode scheme="halTreeTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>In this paper, we consider Langevin processes with mechanical constraints. The latter are a fundamental tool in molecular dynamics simulation for sampling purposes and for the computation of free energy differences. The results of this paper can be divided into three parts. (i) We propose a simple discretization of the constrained Langevin process based on a standard splitting strategy. We show how to correct the scheme so that it samples {\em exactly} the canonical measure restricted on a submanifold, using a Metropolis rule in the spirit of the Generalized Hybrid Monte Carlo (GHMC) algorithm. Moreover, we obtain, in some limiting regime, a consistent discretization of the overdamped Langevin (Brownian) dynamics on a submanifold, also sampling exactly the correct canonical measure with constraints. The corresponding numerical methods can be used to sample (without any bias) a probability measure supported by a submanifold. (ii) For free energy computation using thermodynamic integration, we rigorously prove that the longtime average of the Lagrange multipliers of the constrained Langevin dynamics yields the gradient of a rigid version of the free energy associated with the constraints. A second order time discretization using the Lagrange multipliers is proposed. (iii) The Jarzynski-Crooks fluctuation relation is proved for Langevin processes with mechanical constraints evolving in time. An original numerical discretization without time-step error is proposed. Numerical illustrations are provided for (ii) and (iii).</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-51621" status="OLD">
          <idno type="IdRef">151174822</idno>
          <idno type="ISNI">0000000403826254</idno>
          <idno type="RNSR">200320607R</idno>
          <idno type="ROR">https://ror.org/03wct8w46</idno>
          <idno type="Wikidata">Q51781803</idno>
          <orgName>Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique</orgName>
          <orgName type="acronym">CERMICS</orgName>
          <date type="end">2024-12-31</date>
          <desc>
            <address>
              <addrLine>6 et 8 avenue Blaise Pascal Cité Descartes - Champs sur Marne 77455 Marne la Vallée Cedex 2</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://cermics.enpc.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-301545" type="direct"/>
          </listRelation>
        </org>
        <org type="researchteam" xml:id="struct-2429" status="OLD">
          <idno type="RNSR">200218327S</idno>
          <orgName>Methods and engineering of multiscale computing from atom to continuum</orgName>
          <orgName type="acronym">MICMAC</orgName>
          <desc>
            <address>
              <country key="FR"/>
            </address>
          </desc>
          <listRelation>
            <relation active="#struct-86790" type="direct"/>
            <relation active="#struct-300009" type="indirect"/>
            <relation active="#struct-301545" type="direct"/>
          </listRelation>
        </org>
        <org type="researchteam" xml:id="struct-56018" status="OLD">
          <idno type="RNSR">200718287B</idno>
          <orgName>SImulations and Modeling for PArticles and Fluids</orgName>
          <orgName type="acronym">SIMPAF</orgName>
          <date type="end">2013-12-31</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/equipes/simpaf</ref>
          </desc>
          <listRelation>
            <relation active="#struct-32" type="direct"/>
            <relation name="UMR8524" active="#struct-374570" type="indirect"/>
            <relation name="UMR8524" active="#struct-441569" type="indirect"/>
            <relation active="#struct-104752" type="direct"/>
            <relation active="#struct-300009" type="indirect"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-301545" status="OLD">
          <idno type="ROR">https://ror.org/02nwvxz07</idno>
          <orgName>École nationale des ponts et chaussées</orgName>
          <orgName type="acronym">ENPC</orgName>
          <date type="start">1747-02-14</date>
          <date type="end">2024-12-31</date>
          <desc>
            <address>
              <addrLine>École nationale des ponts et chaussées, 6-8 avenue Blaise-Pascal, Cité Descartes, Champs-sur-Marne, 77455 Marne-la-Vallée cedex 2</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://ecoledesponts.fr/</ref>
          </desc>
        </org>
        <org type="laboratory" xml:id="struct-86790" status="OLD">
          <orgName>Inria Paris-Rocquencourt</orgName>
          <date type="end">2016-03-30</date>
          <desc>
            <address>
              <addrLine>INRIA Rocquencourt : Domaine de Voluceau, Rocquencourt B.P. 105 78153 le Chesnay Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/centre/paris-rocquencourt</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300009" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-300009" status="VALID">
          <idno type="ROR">https://ror.org/02kvxyf05</idno>
          <orgName>Institut National de Recherche en Informatique et en Automatique</orgName>
          <orgName type="acronym">Inria</orgName>
          <desc>
            <address>
              <addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/en/</ref>
          </desc>
        </org>
        <org type="laboratory" xml:id="struct-32" status="VALID">
          <idno type="IdRef">161603971</idno>
          <idno type="ISNI">0000000403684081</idno>
          <idno type="RNSR">199812852H</idno>
          <idno type="ROR">https://ror.org/043n4fm24</idno>
          <idno type="Wikidata">Q3214464</idno>
          <orgName>Laboratoire Paul Painlevé - UMR 8524</orgName>
          <orgName type="acronym">LPP</orgName>
          <date type="start">2004-01-01</date>
          <desc>
            <address>
              <addrLine>Université de Lille - Sciences et technologies - U.F.R. de Mathématiques - 59655 Villeneuve d'Ascq Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://math.univ-lille.fr/</ref>
          </desc>
          <listRelation>
            <relation name="UMR8524" active="#struct-374570" type="direct"/>
            <relation name="UMR8524" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-374570" status="VALID">
          <idno type="IdRef">223446556</idno>
          <idno type="ISNI">0000 0001 2242 6780</idno>
          <idno type="ROR">https://ror.org/02kzqn938</idno>
          <idno type="Wikidata">Q3551621</idno>
          <orgName>Université de Lille</orgName>
          <desc>
            <address>
              <addrLine>EPE Université de Lille. -- 42 rue Paul Duez, 59000 Lille</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.univ-lille.fr/</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-441569" status="VALID">
          <idno type="IdRef">02636817X</idno>
          <idno type="ISNI">0000000122597504</idno>
          <idno type="ROR">https://ror.org/02feahw73</idno>
          <orgName>Centre National de la Recherche Scientifique</orgName>
          <orgName type="acronym">CNRS</orgName>
          <date type="start">1939-10-19</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.cnrs.fr/</ref>
          </desc>
        </org>
        <org type="laboratory" xml:id="struct-104752" status="VALID">
          <idno type="RNSR">200818245B</idno>
          <idno type="ROR">https://ror.org/04eej9726</idno>
          <orgName>Centre Inria de l'Université de Lille</orgName>
          <desc>
            <address>
              <addrLine>Parc Scientifique de la Haute Borne 40, avenue Halley Bât.A, Park Plaza 59650 Villeneuve d'Ascq</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/lille/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300009" type="direct"/>
          </listRelation>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>