Thumbnail

Fourier's law for a microscopic model of heat conduction

Olla, Stefano; Bernardin, Cédric (2005), Fourier's law for a microscopic model of heat conduction, Journal of Statistical Physics, 121, 3-4, p. 271-289. http://dx.doi.org/10.1007/s10955-005-7578-9

View/Open
Type
Article accepté pour publication ou publié
Date
2005
Journal name
Journal of Statistical Physics
Volume
121
Number
3-4
Publisher
Springer
Pages
271-289
Publication identifier
Metadata
Show full item record
Author(s)
Olla, Stefano cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Bernardin, Cédric
Abstract (EN)
We consider a chain of N harmonic oscillators perturbed by a conservative stochastic dynamics and coupled at the boundaries to two gaussian thermostats at different temperatures. The stochastic perturbation is given by a diffusion process that exchange momentum between nearest neighbor oscillators conserving the total kinetic energy. The resulting total dynamics is a degenerate hypoelliptic diffusion with a smooth stationary state. We prove that the stationary state, in the limit as N→ ∞, satisfies Fourier’s law and the linear profile for the energy average.
Subjects / Keywords
non-equilibrium stationary; entropy production; heat conduction; Fourier’s law