Multi-level Dynamical Systems: Connecting the Ruelle Response Theory and the Mori-Zwanzig Approach.
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| Title: | Multi-level Dynamical Systems: Connecting the Ruelle Response Theory and the Mori-Zwanzig Approach. |
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| Authors: | Wouters, Jeroen1 jeroen.wouters@uni-hamburg.de, Lucarini, Valerio |
| Source: | Journal of Statistical Physics. Jun2013, Vol. 151 Issue 5, p850-860. 11p. 1 Diagram. |
| Subjects: | Dynamical systems, Ruelle operators, Operator product expansions, Stochastic processes, Statistical mechanics, Computational complexity, Mathematical models |
| Abstract: | We consider the problem of deriving approximate autonomous dynamics for a number of variables of a dynamical system, which are weakly coupled to the remaining variables. In a previous paper we have used the Ruelle response theory on such a weakly coupled system to construct a surrogate dynamics, such that the expectation value of any observable agrees, up to second order in the coupling strength, to its expectation evaluated on the full dynamics. We show here that such surrogate dynamics agree up to second order to an expansion of the Mori-Zwanzig projected dynamics. This implies that the parametrizations of unresolved processes suited for prediction and for the representation of long term statistical properties are closely related, if one takes into account, in addition to the widely adopted stochastic forcing, the often neglected memory effects. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Statistical Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Items | – Name: Title Label: Title Group: Ti Data: Multi-level Dynamical Systems: Connecting the Ruelle Response Theory and the Mori-Zwanzig Approach. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Wouters%2C+Jeroen%22">Wouters, Jeroen</searchLink><relatesTo>1</relatesTo><i> jeroen.wouters@uni-hamburg.de</i><br /><searchLink fieldCode="AR" term="%22Lucarini%2C+Valerio%22">Lucarini, Valerio</searchLink> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Statistical+Physics%22">Journal of Statistical Physics</searchLink>. Jun2013, Vol. 151 Issue 5, p850-860. 11p. 1 Diagram. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Dynamical+systems%22">Dynamical systems</searchLink><br /><searchLink fieldCode="DE" term="%22Ruelle+operators%22">Ruelle operators</searchLink><br /><searchLink fieldCode="DE" term="%22Operator+product+expansions%22">Operator product expansions</searchLink><br /><searchLink fieldCode="DE" term="%22Stochastic+processes%22">Stochastic processes</searchLink><br /><searchLink fieldCode="DE" term="%22Statistical+mechanics%22">Statistical mechanics</searchLink><br /><searchLink fieldCode="DE" term="%22Computational+complexity%22">Computational complexity</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+models%22">Mathematical models</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We consider the problem of deriving approximate autonomous dynamics for a number of variables of a dynamical system, which are weakly coupled to the remaining variables. In a previous paper we have used the Ruelle response theory on such a weakly coupled system to construct a surrogate dynamics, such that the expectation value of any observable agrees, up to second order in the coupling strength, to its expectation evaluated on the full dynamics. We show here that such surrogate dynamics agree up to second order to an expansion of the Mori-Zwanzig projected dynamics. This implies that the parametrizations of unresolved processes suited for prediction and for the representation of long term statistical properties are closely related, if one takes into account, in addition to the widely adopted stochastic forcing, the often neglected memory effects. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Statistical Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s10955-013-0726-8 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 11 StartPage: 850 Subjects: – SubjectFull: Dynamical systems Type: general – SubjectFull: Ruelle operators Type: general – SubjectFull: Operator product expansions Type: general – SubjectFull: Stochastic processes Type: general – SubjectFull: Statistical mechanics Type: general – SubjectFull: Computational complexity Type: general – SubjectFull: Mathematical models Type: general Titles: – TitleFull: Multi-level Dynamical Systems: Connecting the Ruelle Response Theory and the Mori-Zwanzig Approach. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Wouters, Jeroen – PersonEntity: Name: NameFull: Lucarini, Valerio IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 06 Text: Jun2013 Type: published Y: 2013 Identifiers: – Type: issn-print Value: 00224715 Numbering: – Type: volume Value: 151 – Type: issue Value: 5 Titles: – TitleFull: Journal of Statistical Physics Type: main |
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