In a joint colllaboration with Adriana Neumann and Artur Lopes,
we consider a one-dimensional spin lattice and a fixed observable A so
that the associated Ruelle operator is Markov. We define, canonically
associated to A, a jump process with infinitesimal generator L. We show
how to define a notion of relative entropy of the stationary process
asssociated to a perturbed generator L+V. We then show a large deviation
principle in time of these processes.