Spectral Properties of Effective Dynamics from Conditional Expectations

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dc.citation.articleNumber134en_US
dc.citation.issueNumber2en_US
dc.citation.journalTitleEntropyen_US
dc.citation.volumeNumber23en_US
dc.contributor.authorNüske, Feliksen_US
dc.contributor.authorKoltai, Péteren_US
dc.contributor.authorBoninsegna, Lorenzoen_US
dc.contributor.authorClementi, Ceciliaen_US
dc.contributor.orgCenter for Theoretical Biological Physicsen_US
dc.date.accessioned2021-02-24T19:15:50Zen_US
dc.date.available2021-02-24T19:15:50Zen_US
dc.date.issued2021en_US
dc.description.abstractThe 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.en_US
dc.identifier.citationNüske, Feliks, Koltai, Péter, Boninsegna, Lorenzo, et al.. "Spectral Properties of Effective Dynamics from Conditional Expectations." <i>Entropy,</i> 23, no. 2 (2021) MDPI: https://doi.org/10.3390/e23020134.en_US
dc.identifier.digitalentropy-23-00134-v2en_US
dc.identifier.doihttps://doi.org/10.3390/e23020134en_US
dc.identifier.urihttps://hdl.handle.net/1911/110093en_US
dc.language.isoengen_US
dc.publisherMDPIen_US
dc.rightsThis is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly citeden_US
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/en_US
dc.subject.keywordstochastic differential equationsen_US
dc.subject.keywordcoarse grainingen_US
dc.subject.keywordinfinitesimal generatoren_US
dc.subject.keywordspectral analysisen_US
dc.subject.keywordextended dynamic mode decompositionen_US
dc.subject.keywordKramers–Moyal formulaeen_US
dc.subject.keywordLangevin dynamicsen_US
dc.titleSpectral Properties of Effective Dynamics from Conditional Expectationsen_US
dc.typeJournal articleen_US
dc.type.dcmiTexten_US
dc.type.publicationpublisher versionen_US
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