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Microscopic derivation of an adiabatic thermodynamic transformation

hal.structure.identifier
dc.contributor.authorOlla, Stefano
HAL ID: 18345
ORCID: 0000-0003-0845-1861		*
hal.structure.identifier
dc.contributor.authorSimon, Marielle
HAL ID: 7207		*
dc.date.accessioned2014-10-01T14:33:45Z
dc.date.available2014-10-01T14:33:45Z
dc.date.issued2015
dc.identifier.issn0103-0752
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/13975
dc.language.isoenen
dc.subjectquasi static trasformations
dc.subjecthydrodynamic limit
dc.subjectthermodynamic entropy
dc.subjectAdiabatic thermodynamic transformations
dc.subject.ddc519en
dc.titleMicroscopic derivation of an adiabatic thermodynamic transformation
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherUnité de Mathématiques Pures et Appliquées (UMPA-ENSL) http://www.umpa.ens-lyon.fr/;France
dc.description.abstractenWe obtain macroscopic adiabatic thermodynamic transformations by space-time scalings of a microscopic Hamiltonian dynamics subject to random collisions with the environment. The microscopic dynamics is given by a chain of oscillators subject to a varying tension (external force) and to collisions with external independent particles of ''infinite mass''. The effect of each collision is to change the sign of the velocity without changing the modulus. This way the energy is conserved by the resulting dynamics. After a diffusive space-time scaling and cross-graining, the profiles of volume and energy converge to the solution of a deterministic diffusive system of equations with boundary conditions given by the applied tension. This defines an irreversible thermodynamic transformation from an initial equilibrium to a new equilibrium given by the final tension applied. Quasi-static reversible adiabatic transformations are then obtained by a further time scaling. Then we prove that the relations between the limit work, internal energy and thermodynamic entropy agree with the first and second principle of thermodynamics.
dc.relation.isversionofjnlnameBrazilian Journal of Probability and Statistics
dc.relation.isversionofjnlvol29
dc.relation.isversionofjnlissue2
dc.relation.isversionofjnldate2015
dc.relation.isversionofjnlpages540-564
dc.relation.isversionofdoi10.1214/14-BJPS275
dc.identifier.urlsitehttps://arxiv.org/abs/1409.6424v2
dc.relation.isversionofjnlpublisherN. Zanichelli
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.description.submittednonen
dc.description.ssrncandidatenon
dc.description.halcandidateoui
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2016-07-22T12:29:01Z
hal.author.functionaut
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