Stationary non-equilibrium properties for a heat conduction model

Details Stationary non-equilibrium properties for a heat conduction model Stationary non-equilibrium properties for a heat conduction model

2008-08-05

arxiv.org/abs/0808.0662v1

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1103/PhysRevE.78.021134

We consider a stochastic heat conduction model for solids composed by N interacting atoms. The system is in contact with two heat baths at different temperature $T_\ell$ and $T_r$. The bulk dynamics conserve two quantities: the energy and the deformation between atoms. If $T_\ell \neq T_r$, a heat flux takes place in the system. For large $N$, the system adopts a linear temperature profile between $T_\ell$ and $T_r$. We establish the hydrodynamic limit for the two conserved quantities. We introduce the fluctuations field of the energy and of the deformation in the non-equilibrium steady state. As $N$ goes to infinity, we show that this field converges to a Gaussian field and we compute the limiting covariance matrix. The main contribution of the paper is the study of large deviations for the temperature profile in the non-equilibrium stationary state. A variational formula for the rate function is derived following the recent macroscopic fluctuation theory of Bertini et al.

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