Large Deviations for a Stochastic Model of Heat Flow |
| |
Authors: | Lorenzo Bertini Davide Gabrielli Joel L Lebowitz |
| |
Institution: | (1) Dipartimento di Matematica, Università di Roma La Sapienza, P.le A. Moro 2, 00185 Roma, Italy;(2) Dipartimento di Matematica, Università dell’Aquila, 67100 Coppito, L’Aquila, Italy;(3) Department of Mathematics and Physics, Rutgers University, New Brunswick, NJ 08903, USA |
| |
Abstract: | 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 et al. (J. Statist. Phys., 27:65–74 (1982).) 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
, 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
. 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
models and find the features common in these two and other models whose S(θ) is known. |
| |
Keywords: | Stationary nonequilibrium states large deviations boundary driven stochastic systems |
本文献已被 SpringerLink 等数据库收录! |
|