Fluctuations in stationary nonequilibrium states of irreversible processes

We formulate a dynamical fluctuation theory for stationary nonequilibrium states (SNS) which covers situations in a nonlinear hydrodynamic regime and is verified explicitly in stochastic models of interacting particles. In our theory a crucial role is played by the time reversed dynamics. Our results include the modification of the Onsager-Machlup theory in the SNS, a general Hamilton-Jacobi equation for the macroscopic entropy and a nonequilibrium, nonlinear fluctuation dissipation relation valid for a wide class of systems.