Exact fluctuations of nonequilibrium steady states from approximate auxiliary dynamics

We describe a framework to significantly reduce the computational effort to evaluate large deviation functions of time integrated observables within nonequilibrium steady states. We do this by incorporating an auxiliary dynamics into trajectory based Monte Carlo calculations, through a transformation of the system's propagator using an approximate guiding function. This procedure importance samples the trajectories that most contribute to the large deviation function, mitigating the exponentially complexity of such calculations. We illustrate the method by studying driven diffusions and interacting lattice models in one and two dimensions. Our work offers an avenue to calculate large deviation functions for high dimensional systems driven far from equilibrium.