Journal
JOURNAL OF STATISTICAL PHYSICS
Volume 121, Issue 3-4, Pages 271-289Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10955-005-7578-9
Keywords
Fourier's law; heat conduction; entropy production; non-equilibrium stationary state
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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 ->proportional to, satisfies Fourier's law and the linear profile for the energy average.
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