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  <doc>
    <id>1894</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2013-07-11</completedDate>
    <publishedDate>2013-07-11</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Linear response theory and optimal control for a molecular system under nonequilibrium conditions</title>
    <abstract language="eng">In this paper, we propose a straightforward generalization of linear&#13;
response theory to systems in nonequilibrium that are subject to&#13;
nonequilibrium driving. We briefly revisit the standard linear response&#13;
result for equilibrium systems, where we consider Langevin dynamics&#13;
as a special case, and then give an alternative derivation using a&#13;
change-of-measure argument that does not rely on any stationarity or&#13;
reversibility assumption. This procedure moreover easily enables us&#13;
to calculate the second order correction to the linear response formula&#13;
(which may or may not be useful in practice). Furthermore, we outline&#13;
how the novel nonequilibirum linear response formula can be used to&#13;
compute optimal controls of molecular systems for cases in which one&#13;
wants to steer the system to maximize a certain target expectation&#13;
value. We illustrate our approach with simple numerical examples.</abstract>
    <identifier type="urn">urn:nbn:de:0297-zib-18944</identifier>
    <enrichment key="SourceTitle">Appeared in: Molecular Physics 111 (2013) 3555-3564</enrichment>
    <author>Han Wang</author>
    <submitter>Erlinda Körnig</submitter>
    <author>Carsten Hartmann</author>
    <author>Christof Schütte</author>
    <series>
      <title>ZIB-Report</title>
      <number>13-33</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>nonequilibrium molecular dynamics</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>linear response</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Girsanov transformation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>stochastic control</value>
    </subject>
    <collection role="msc" number="65C35">Stochastic particle methods [See also 82C80]</collection>
    <collection role="msc" number="82C31">Stochastic methods (Fokker-Planck, Langevin, etc.) [See also 60H10]</collection>
    <collection role="msc" number="93E20">Optimal stochastic control</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1894/ZR-13-33.pdf</file>
  </doc>
</export-example>
