Repository: Freie Universität Berlin, Math Department

A weak characterization of slow variables in stochastic dynamical systems

Bittracher, Andreas and Schütte, Christof (2020) A weak characterization of slow variables in stochastic dynamical systems. SFB 1114 Preprint in arXive . pp. 1-20. ISSN 2005.01631 (Submitted)

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Official URL: https://arxiv.doi.org/abs/2005.01631

Abstract

We present a novel characterization of slow variables for continuous Markov processes that provably preserve the slow timescales. These slow variables are known as reaction coordinates in molecular dynamical applications, where they play a key role in system analysis and coarse graining. The defining characteristics of these slow variables is that they parametrize a so-called transition manifold, a low-dimensional manifold in a certain density function space that emerges with progressive equilibration of the system's fast variables. The existence of said manifold was previously predicted for certain classes of metastable and slow-fast systems. However, in the original work, the existence of the manifold hinges on the pointwise convergence of the system's transition density functions towards it. We show in this work that a convergence in average with respect to the system's stationary measure is sufficient to yield reaction coordinates with the same key qualities. This allows one to accurately predict the timescale preservation in systems where the old theory is not applicable or would give overly pessimistic results. Moreover, the new characterization is still constructive, in that it allows for the algorithmic identification of a good slow variable. The improved characterization, the error prediction and the variable construction are demonstrated by a small metastable system.

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics
ID Code:2438
Deposited By: Monika Drueck
Deposited On:25 May 2020 12:50
Last Modified:25 May 2020 12:50

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