An open microscopic model of heat conduction: evolution and non-equilibrium stationary states
Komorowski, Tomasz; Olla, Stefano; Simon, Marielle (2020), An open microscopic model of heat conduction: evolution and non-equilibrium stationary states, Communications in Mathematical Sciences, 18, 3, p. 751-780. 10.4310/CMS.2020.v18.n3.a8
TypeArticle accepté pour publication ou publié
Journal nameCommunications in Mathematical Sciences
MetadataShow full item record
Institut of Mathematics - Polish Academy of Sciences [PAN]
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Inria Lille - Nord Europe
Abstract (EN)We 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.
Subjects / KeywordsHamiltonian dynamic; evolution and non-equilibrium stationary states; open chain of oscillator; heat conduction; uphill heat diffusion
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Macroscopic evolution of mechanical and thermal energy in a harmonic chain with random flip of velocities Olla, Stefano; Simon, Marielle; Komorowski, Tomasz (2018) Article accepté pour publication ou publié