hal.structure.identifier School of Mathematics - Georgia Institute of Technology dc.contributor.author Bonetto, Federico * hal.structure.identifier CEntre de REcherches en MAthématiques de la DEcision [CEREMADE] dc.contributor.author Olla, Stefano HAL ID: 18345 ORCID: 0000-0003-0845-1861 * hal.structure.identifier dc.contributor.author Lukkarinen, Jani * hal.structure.identifier Center for Mathematical Sciences Research dc.contributor.author Lebowitz, Joel L. * dc.date.accessioned 2009-07-06T09:38:49Z dc.date.available 2009-07-06T09:38:49Z dc.date.issued 2009 dc.identifier.uri https://basepub.dauphine.fr/handle/123456789/786 dc.language.iso en en dc.subject non-equilibrium stationary state dc.subject entropy production dc.subject self-consistent thermostats dc.subject Green-Kubo formula dc.subject Thermal condutivity en dc.subject.ddc 519 en dc.title Heat Conduction and Entropy Production in Anharmonic Crystals with Self-Consistent Stochastic Reservoirs en dc.type Article accepté pour publication ou publié dc.contributor.editoruniversityother University of Helsinki;Finlande dc.contributor.editoruniversityother Georgia Institute of Technology;États-Unis dc.contributor.editoruniversityother Rutgers University;États-Unis dc.description.abstracten We 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.isversionofjnlname Journal of Statistical Physics dc.relation.isversionofjnlvol 134 en dc.relation.isversionofjnlissue 5 en dc.relation.isversionofjnldate 2009-04 dc.relation.isversionofjnlpages 1097 en dc.relation.isversionofdoi http://dx.doi.org/10.1007/s10955-008-9657-1 en dc.identifier.urlsite http://hal.archives-ouvertes.fr/hal-00318755/en/ en dc.description.sponsorshipprivate oui en dc.relation.isversionofjnlpublisher Springer dc.subject.ddclabel Probabilités et mathématiques appliquées en hal.author.function aut hal.author.function aut hal.author.function aut hal.author.function aut
﻿

## Files in this item

FilesSizeFormatView

There are no files associated with this item.