04-6 Jean-Pierre Eckmann, Lai-Sang Young

Unraveling the Fourier Law for Hamiltonian Systems (168K, postscript) Jan 19, 04

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Abstract. We exhibit simple Hamiltonian and stochastic models of heat transport in non-equilibrium problems. Theoretical arguments are given to show that, for a wide class of models, the temperature profile obeys a universal law depending on a parameter $\alpha $. When $\alpha=1$, the law is linear, but, depending on the nature of the energy exchange mechanism by tracer particles, we find that $\alpha $ is, in many cases, different from 1. When $\alpha \neq 1$, the temperature profile is not linear, although translation invariance and, in some models, local thermal equilibrium, hold.

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