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Linear response theory and optimal control for a molecular system under nonequilibrium conditions

Please always quote using this URN: urn:nbn:de:0297-zib-18944
  • In this paper, we propose a straightforward generalization of linear response theory to systems in nonequilibrium that are subject to nonequilibrium driving. We briefly revisit the standard linear response result for equilibrium systems, where we consider Langevin dynamics as a special case, and then give an alternative derivation using a change-of-measure argument that does not rely on any stationarity or reversibility assumption. This procedure moreover easily enables us to calculate the second order correction to the linear response formula (which may or may not be useful in practice). Furthermore, we outline how the novel nonequilibirum linear response formula can be used to compute optimal controls of molecular systems for cases in which one wants to steer the system to maximize a certain target expectation value. We illustrate our approach with simple numerical examples.

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Author:Han Wang, Carsten HartmannORCiD, Christof Schütte
Document Type:ZIB-Report
Tag:Girsanov transformation; linear response; nonequilibrium molecular dynamics; stochastic control
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Cxx Probabilistic methods, simulation and stochastic differential equations (For theoretical aspects, see 68U20 and 60H35) / 65C35 Stochastic particle methods [See also 82C80]
82-XX STATISTICAL MECHANICS, STRUCTURE OF MATTER / 82Cxx Time-dependent statistical mechanics (dynamic and nonequilibrium) / 82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) [See also 60H10]
93-XX SYSTEMS THEORY; CONTROL (For optimal control, see 49-XX) / 93Exx Stochastic systems and control / 93E20 Optimal stochastic control
Date of first Publication:2013/07/11
Series (Serial Number):ZIB-Report (13-33)
Published in:Appeared in: Molecular Physics 111 (2013) 3555-3564
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