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 ¯ 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 models and find the features common in these two and other models whose S(θ) is known

Large deviations for a stochastic model of heat flow

GABRIELLI, DAVIDE;
2005-01-01

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 ¯ 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 models and find the features common in these two and other models whose S(θ) is known
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/18808
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 88
  • ???jsp.display-item.citation.isi??? 83
social impact