5,666 research outputs found

    Large deviations for a stochastic model of heat flow

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    We investigate a one dimensional chain of 2N2N harmonic oscillators in which neighboring sites have their energies redistributed randomly. The sites N-N and NN are in contact with thermal reservoirs at different temperature τ\tau_- and τ+\tau_+. Kipnis, Marchioro, and Presutti \cite{KMP} proved that this model satisfies {}Fourier's law and that in the hydrodynamical scaling limit, when NN \to \infty, the stationary state has a linear energy density profile θˉ(u)\bar \theta(u), u[1,1]u \in [-1,1]. We derive the large deviation function S(θ(u))S(\theta(u)) for the probability of finding, in the stationary state, a profile θ(u)\theta(u) different from θˉ(u)\bar \theta(u). The function S(θ)S(\theta) 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)S(\theta) is known.Comment: 28 pages, 0 figure

    Level 2.5 large deviations for continuous time Markov chains with time periodic rates

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    We consider an irreducible continuous time Markov chain on a finite state space and with time periodic jump rates and prove the joint large deviation principle for the empirical measure and flow and the joint large deviation principle for the empirical measure and current. By contraction we get the large deviation principle of three types of entropy production flow. We derive some Gallavotti-Cohen duality relations and discuss some applications.Comment: 37 pages. corrected versio
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