2005/01/27 by Lorenzo Bertini, Davide Gabrielli, Joel L. Lebowitz · 6 citations
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1007/s10955-005-5527-2
28 pages, 0 figures
arxiv created 2005/01/27 · openalex publication_date 2005/09/17 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We investigate a one dimensional chain of 2N harmonic oscillators in which neighboring sites have their energies redistributed randomly. The sites -N and N are in contact with thermal reservoirs at different temperature τ- and τ+. Kipnis, Marchioro, and Presutti \citeKMP proved that this model satisfies Fourier's law and that in the hydrodynamical scaling limit, when N → ∞, the stationary state has a linear energy density profile θ(u), u ∈ [-1,1]. We derive the large deviation function S(θ(u)) for the probability of finding, in the stationary state, a profile θ(u) different from θ(u). The function S(θ) has striking similarities to, but also large differences from, the corresponding one of the symmetric exclusion process. Like the latter it is nonlocal and satisfies a variational equation. Unlike the latter it is not convex and the Gaussian normal fluctuations are enhanced rather than suppressed compared to the local equilibrium state. We also briefly discuss more general model and find the features common in these two and other models whose S(θ) is known.