https://hal-cea.archives-ouvertes.fr/cea-01113482Bauer, MichelMichelBauerIPHT - Institut de Physique Théorique - UMR CNRS 3681 - CEA - Commissariat à l'énergie atomique et aux énergies alternatives - Université Paris-Saclay - CNRS - Centre National de la Recherche ScientifiqueLPTENS - Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure] - FRDPENS - Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - CNRS - Centre National de la Recherche Scientifique - UPMC - Université Pierre et Marie Curie - Paris 6 - CNRS - Centre National de la Recherche ScientifiqueCornu, FrançoiseFrançoiseCornuLPT - Laboratoire de Physique Théorique d'Orsay [Orsay] - UP11 - Université Paris-Sud - Paris 11 - CNRS - Centre National de la Recherche ScientifiqueLocal detailed balance: a microscopic derivationHAL CCSD2014[PHYS.MPHY] Physics [physics]/Mathematical Physics [math-ph]De Laborderie, Emmanuelle2015-02-05 15:43:322023-02-10 03:47:482015-02-05 15:43:32enJournal articles10.1088/1751-8113/48/1/0150081Thermal contact is the archetype of non-equilibrium processes driven by constant non-equilibrium constraints when the latter are enforced by reservoirs exchanging conserved microscopic quantities. At a mesoscopic scale only the energies of the macroscopic bodies are accessible together with the configurations of the contact system. We consider a class of models where the contact system, as well as macroscopic bodies, have a finite number of possible configurations. The global system with only discrete degrees of freedom has no microscopic Hamiltonian dynamics, but it is shown that, if the microscopic dynamics is assumed to be deterministic and ergodic and to conserve energy according to some specific pattern, and if the mesoscopic evolution of the global system is approximated by a Markov process as closely as possible, then the mesoscopic transition rates obey three constraints. In the limit where macroscopic bodies can be considered as reservoirs at thermodynamic equilibrium (but with different intensive parameters) the mesoscopic transition rates turn into transition rates for the contact system and the third constraint becomes local detailed balance ; the latter is generically expressed in terms of the microscopic exchange entropy variation, namely the opposite of the variation of the thermodynamic entropy of the reservoir involved in a given microscopic jump of the contact system configuration. For a finite-time evolution after contact has been switched on we derive a fluctuation relation for the joint probability of the heat amounts received from the various reservoirs. The generalization to systems exchanging energy, volume and matter with several reservoirs, with a possible conservative external force acting on the contact system, is given explicitly.