Repository: Freie Universität Berlin, Math Department

Spectral Properties of Effective Dynamics from Conditional Expectations

Nüske, Feliks and Koltai, Péter and Boninsegna, Lorenzo and Clementi, Cecilia (2021) Spectral Properties of Effective Dynamics from Conditional Expectations. Entropy, 23 (134). pp. 1-25.

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Abstract: The reduction of high-dimensional systems to effective models on a smaller set of variables is an essential task in many areas of science. For stochastic dynamics governed by diffusion processes, a general procedure to find effective equations is the conditioning approach. In this paper, we are interested in the spectrum of the generator of the resulting effective dynamics, and how it compares to the spectrum of the full generator. We prove a new relative error bound in terms of the eigenfunction approximation error for reversible systems. We also present numerical examples indicating that, if Kramers–Moyal (KM) type approximations are used to compute the spectrum of the reduced generator, it seems largely insensitive to the time window used for the KM estimators. We analyze the implications of these observations for systems driven by underdamped Langevin dynamics, and show how meaningful effective dynamics can be defined in this setting.

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics > BioComputing Group
ID Code:2594
Deposited By: Monika Drueck
Deposited On:27 Aug 2021 13:43
Last Modified:25 Oct 2021 20:35

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