Small noise asymptotic of the Gallavotti-Cohen functional for diffusion processes

Abstract

We consider, for a diffusion process in R^n, the Gallavotti-Cohen functional, defined as the empirical power dissipated in a time interval by the non-conservative part of the drift. We prove a large deviation principle in the limit in which the noise vanishes and the time interval diverges. The corresponding rate functional, which satisfies the fluctuation theorem, is expressed in terms of a variational problem on the classical Freidlin-Wentzell functional.

20 pages

References in corpus (2)

• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Gallavotti-Cohen theorem, Chaotic Hypothesis and the zero-noise limit