Journal of Statistical Physics

, Volume 121, Issue 3–4, pp 271–289

Fourier’s Law for a Microscopic Model of Heat Conduction



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


Fourier’s law heat conduction entropy production non-equilibrium stationary state 


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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Département de mathématiquesEns de CachanFranceCachan
  2. 2.Ceremade, UMR CNRS 7534Université de Paris DauphineParis Cedex 16France

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