ABSTRACT:

Consider a diffusion process in R^n. It has been shown that a suitable functional on the path space, interpreted as the production of Gibbs entropy, has a large deviation rate function, as time diverges, which satisfies the fluctuation theorem of Gallavotti and Cohen. For a particular class of non reversible diffusions, I will consider the small noise asymptotic of such rate function and show that it can be expressed in terms of a suitable variational problem. Some simple examples in which this limiting functional can be written in a closed form are finally discussed.