On microscopic origins of generalized gradient structures
dc.bibliographicCitation.seriesTitle | WIAS Preprints | eng |
dc.bibliographicCitation.volume | 2148 | |
dc.contributor.author | Liero, Matthias | |
dc.contributor.author | Mielke, Alexander | |
dc.contributor.author | Peletier, Mark A. | |
dc.contributor.author | Renger, D.R. Michiel | |
dc.date.accessioned | 2016-12-13T10:46:44Z | |
dc.date.available | 2019-06-28T08:24:15Z | |
dc.date.issued | 2015 | |
dc.description.abstract | Classical gradient systems have a linear relation between rates and driving forces. In generalized gradient systems we allow for arbitrary relations derived from general non-quadratic dissipation potentials. This paper describes two natural origins for these structures. A first microscopic origin of generalized gradient structures is given by the theory of large-deviation principles. While Markovian diffusion processes lead to classical gradient structures, poissonian jump processes give rise to cosh-type dissipation potentials. A second origin arises via a new form of convergence, that we call EDP-convergence. Even when starting with classical gradient systems, where the dissipation potential is a quadratic functional of the rate, we may obtain a generalized gradient system in the evolutionary Gamma-limit. As examples we treat (i) the limit of a diffusion equation having a thin layer of low diffusivity, which leads to a membrane model, and (ii) the limit of diffusion over a high barrier, which gives a reaction-diffusion system. | eng |
dc.description.version | publishedVersion | eng |
dc.format | application/pdf | |
dc.identifier.issn | 2198-5855 | |
dc.identifier.uri | https://doi.org/10.34657/2824 | |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/3398 | |
dc.language.iso | eng | eng |
dc.publisher | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik | eng |
dc.relation.issn | 0946-8633 | eng |
dc.rights.license | This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. | eng |
dc.rights.license | Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. | ger |
dc.subject.ddc | 510 | eng |
dc.subject.other | Generalized gradient structure | eng |
dc.subject.other | gradient system | eng |
dc.subject.other | evolutionary Gamma-convergence | eng |
dc.subject.other | energydissipation principle | eng |
dc.subject.other | variational evolution | eng |
dc.subject.other | relative entropy | eng |
dc.subject.other | large-deviation principle | eng |
dc.title | On microscopic origins of generalized gradient structures | eng |
dc.type | Report | eng |
dc.type | Text | eng |
tib.accessRights | openAccess | eng |
wgl.contributor | WIAS | eng |
wgl.subject | Mathematik | eng |
wgl.type | Report / Forschungsbericht / Arbeitspapier | eng |
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