## A multi scale perturbation expansion approach for Markov state modeling of non-stationary molecular dynamics

Please always quote using this URN: urn:nbn:de:0297-zib-64868

- We investigate metastable dynamical systems subject to non-stationary forcing as they appear in molecular dynamics for systems driven by external fields. We show, that if the strength of the forcing is inversely proportional to the length of the slow metastable time scales of the unforced system, then the effective behavior of the forced system on slow time scales can be described by a low-dimensional reduced master equation. Our construction is explicit and uses the multiscale perturbation expansion method called two-timing, or method of multiple scales. The reduced master equation—a Markov state model—can be assembled by constructing two equilibrium Markov state models; one for the unforced system, and one for a slightly perturbed one.

Author: | Péter Koltai, Christof Schütte |
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Document Type: | ZIB-Report |

Tag: | Markov state model; metastability; non-equilibrium molecular dynamics; non-stationary forcing; two timescale master equation |

MSC-Classification: | 34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Exx Asymptotic theory / 34E13 Multiple scale methods |

60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Jxx Markov processes / 60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) [See also 90B30, 91D10, 91D35, 91E40] | |

60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Jxx Markov processes / 60J60 Diffusion processes [See also 58J65] | |

Date of first Publication: | 2017/09/08 |

Series (Serial Number): | ZIB-Report (17-49) |

ISSN: | 1438-0064 |