NON-EQUILIBRIUM POTENTIALS FOR DYNAMICAL SYSTEMS WEAKLY PERTURBED BY NOISE

For dynamical systems perturbed by weak noise, satisfying a large deviation condition, “non-equilibrium potentials” can be defined, whose properties generalize well-known ones of thermodynamic potentials in thermodynamic equilibrium: they are related to the invariant probability density in a familiar way and can serve as Lyapunov functions for the unperturbed dynamical system. In the present article we review recent progress in the study of non-equilibrium potentials for dynamical systems described by one- and two-dimensional maps, including examples with fractal attractors and repellers.