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Heat Conduction and Entropy Production in Anharmonic Crystals with Self-Consistent Stochastic Reservoirs

hal.structure.identifierSchool of Mathematics - Georgia Institute of Technology
dc.contributor.authorBonetto, Federico*
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.identifier
dc.contributor.authorLukkarinen, Jani*
hal.structure.identifierCenter for Mathematical Sciences Research
dc.contributor.authorLebowitz, Joel L.*
dc.date.accessioned2009-07-06T09:38:49Z
dc.date.available2009-07-06T09:38:49Z
dc.date.issued2009
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/786
dc.language.isoenen
dc.subjectnon-equilibrium stationary state
dc.subjectentropy production
dc.subjectself-consistent thermostats
dc.subjectGreen-Kubo formula
dc.subjectThermal condutivityen
dc.subject.ddc519en
dc.titleHeat Conduction and Entropy Production in Anharmonic Crystals with Self-Consistent Stochastic Reservoirsen
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherUniversity of Helsinki;Finlande
dc.contributor.editoruniversityotherGeorgia Institute of Technology;États-Unis
dc.contributor.editoruniversityotherRutgers University;États-Unis
dc.description.abstractenWe investigate a class of anharmonic crystals in $d$ dimensions, $d\ge 1$, coupled to both external and internal heat baths of the Ornstein-Uhlenbeck type. The external heat baths, applied at the boundaries in the $1$-direction, are at specified, unequal, temperatures $\tlb$ and $\trb$. The temperatures of the internal baths are determined in a self-consistent way by the requirement that there be no net energy exchange with the system in the non-equilibrium stationary state (NESS). We prove the existence of such a stationary self-consistent profile of temperatures for a finite system and show it minimizes the entropy production to leading order in $(\tlb -\trb)$. In the NESS the heat conductivity $\kappa$ is defined as the heat flux per unit area divided by the length of the system and $(\tlb -\trb)$. In the limit when the temperatures of the external reservoirs goes to the same temperature $T$, $\kappa(T)$ is given by the Green-Kubo formula, evaluated in an equilibrium system coupled to reservoirs all having the temperature $T$. This $\kappa(T)$ remains bounded as the size of the system goes to infinity. We also show that the corresponding infinite system Green-Kubo formula yields a finite result. Stronger results are obtained under the assumption that the self-consistent profile remains bounded.en
dc.relation.isversionofjnlnameJournal of Statistical Physics
dc.relation.isversionofjnlvol134en
dc.relation.isversionofjnlissue5en
dc.relation.isversionofjnldate2009-04
dc.relation.isversionofjnlpages1097en
dc.relation.isversionofdoihttp://dx.doi.org/10.1007/s10955-008-9657-1en
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00318755/en/en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherSpringer
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
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