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Fourier’s Law for a Microscopic Model of Heat Conduction

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Abstract

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

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Authors and Affiliations

  1. Département de mathématiques, Ens de Cachan, 61 avenue du Président Wilson, 94230, Cachan, France

    Cédric Bernardin

  2. Ceremade, UMR CNRS 7534, Université de Paris Dauphine, Place du Maréchal De Lattre De Tassigny, 75775, Paris Cedex 16, France

    Stefano Olla

Authors
  1. Cédric Bernardin
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  2. Stefano Olla
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Correspondence to Cédric Bernardin.

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Bernardin, C., Olla, S. Fourier’s Law for a Microscopic Model of Heat Conduction. J Stat Phys 121, 271–289 (2005). https://doi.org/10.1007/s10955-005-7578-9

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  • DOI: https://doi.org/10.1007/s10955-005-7578-9

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