TY - GEN A1 - Koltai, Péter A1 - Schütte, Christof T1 - A multi scale perturbation expansion approach for Markov state modeling of non-stationary molecular dynamics N2 - 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. T3 - ZIB-Report - 17-49 KW - Markov state model KW - non-equilibrium molecular dynamics KW - two timescale master equation KW - non-stationary forcing KW - metastability Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-64868 SN - 1438-0064 ER - TY - GEN A1 - Koltai, Peter A1 - Ciccotti, Giovanni A1 - Schütte, Christof T1 - On metastability and Markov state models for non-stationary molecular dynamics BT - 2016 Editor's Choice of The Journal of Chemical Physics T2 - The Journal of Chemical Physics N2 - We utilize the theory of coherent sets to build Markov state models for non- equilibrium molecular dynamical systems. Unlike for systems in equilibrium, “meta- stable” sets in the non-equilibrium case may move as time evolves. We formalize this concept by relying on the theory of coherent sets, based on this we derive finite-time non-stationary Markov state models, and illustrate the concept and its main differences to equilibrium Markov state modeling on simple, one-dimensional examples. T3 - ZIB-Report - 16-11 KW - coherent set, KW - Markov state model KW - non-equilibrium molecular dynamics KW - metastability Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-57869 SN - 1438-0064 VL - 174103 ET - 145 ER -