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On the non-stationary Generalized Langevin Equation

Meyer, Hugues and Voigtmann, Thomas and Schilling, Tanja (2017) On the non-stationary Generalized Langevin Equation. Journal of Chemical Physics, 147, p. 214110. American Institute of Physics (AIP). doi: 10.1063/1.5006980. ISSN 0021-9606.

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In molecular dynamics simulations and single molecule experiments, observables are usually measured along dynamic trajectories and then averaged over an ensemble (bundle) of trajectories. Under stationary conditions, the time-evolution of such averages is described by the generalized Langevin equation. By contrast, if the dynamics is not stationary, it is not a priori clear which form the equation of motion for an averaged observable has. We employ the formalism of time-dependent projection operator techniques to derive the equation of motion for a non-equilibrium trajectory-averaged observable as well as for its non-stationary auto-correlation function. The equation is similar in structure to the generalized Langevin equation but exhibits a time-dependent memory kernel as well as a fluctuating force that implicitly depends on the initial conditions of the process. We also derive a relation between this memory kernel and the autocorrelation function of the fluctuating force that has a structure similar to a fluctuation-dissipation relation. In addition, we show how the choice of the projection operator allows us to relate the Taylor expansion of the memory kernel to data that are accessible in MD simulations and experiments, thus allowing us to construct the equation of motion. As a numerical example, the procedure is applied to Brownian motion initialized in non-equilibrium conditions and is shown to be consistent with direct measurements from simulations.

Item URL in elib:https://elib.dlr.de/116726/
Document Type:Article
Title:On the non-stationary Generalized Langevin Equation
AuthorsInstitution or Email of AuthorsAuthor's ORCID iDORCID Put Code
Meyer, HuguesUniversitè du LuxembourgUNSPECIFIEDUNSPECIFIED
Schilling, TanjaUniversität FreiburgUNSPECIFIEDUNSPECIFIED
Date:6 December 2017
Journal or Publication Title:Journal of Chemical Physics
Refereed publication:Yes
Open Access:No
Gold Open Access:No
In ISI Web of Science:Yes
Page Range:p. 214110
Publisher:American Institute of Physics (AIP)
Keywords:coarse graining, generalized Langevin equation, nonequilibrium dynamics
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Space
HGF - Program Themes:Research under Space Conditions
DLR - Research area:Raumfahrt
DLR - Program:R FR - Research under Space Conditions
DLR - Research theme (Project):R - Material Design and New Materials
Location: Köln-Porz
Institutes and Institutions:Institute of Materials Physics in Space > Scientific Experiments MP
Deposited By: Voigtmann, Dr.rer.nat. Thomas
Deposited On:11 Dec 2017 07:38
Last Modified:08 Mar 2018 18:42

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