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An open microscopic model of heat conduction: evolution and non-equilibrium stationary states

hal.structure.identifierInstitut of Mathematics - Polish Academy of Sciences [PAN]
dc.contributor.authorKomorowski, Tomasz*
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorOlla, Stefano
HAL ID: 18345
ORCID: 0000-0003-0845-1861		*
hal.structure.identifierInria Lille - Nord Europe
dc.contributor.authorSimon, Marielle
HAL ID: 7207		*
dc.date.accessioned2019-12-20T13:00:17Z
dc.date.available2019-12-20T13:00:17Z
dc.date.issued2020
dc.identifier.issn1539-6746
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/20367
dc.language.isoenen
dc.subjectHamiltonian dynamic
dc.subjectevolution and non-equilibrium stationary states
dc.subjectopen chain of oscillator
dc.subjectheat conduction
dc.subjectuphill heat diffusion
dc.subject.ddc519en
dc.titleAn open microscopic model of heat conduction: evolution and non-equilibrium stationary states
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe consider a one-dimensional chain of coupled oscillators in contact at both ends with heat baths at different temperatures, and subject to an external force at one end. The Hamiltonian dynamics in the bulk is perturbed by random exchanges of the neighbouring momenta such that the energy is locally conserved. We prove that in the stationary state the energy and the volume stretch profiles, in large scale limit, converge to the solutions of a diffusive system with Dirichlet boundary conditions. As a consequence the macroscopic temperature stationary profile presents a maximum inside the chain higher than the thermostats temperatures, as well as the possibility of uphill diffusion (energy current against the temperature gradient). Finally, we are also able to derive the non-stationary macroscopic coupled diffusive equations followed by the energy and volume stretch profiles.
dc.relation.isversionofjnlnameCommunications in Mathematical Sciences
dc.relation.isversionofjnlvol18
dc.relation.isversionofjnlissue3
dc.relation.isversionofjnldate2020
dc.relation.isversionofjnlpages751-780
dc.relation.isversionofdoi10.4310/CMS.2020.v18.n3.a8
dc.relation.isversionofjnlpublisherInternational Press
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.forthcomingouien
dc.relation.forthcomingprintouien
dc.description.ssrncandidatenon
dc.description.halcandidatenon
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2020-07-08T12:43:16Z
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