Steady-state distributions and nonsteady dynamics in nonequilibrium systems

We search for steady states in a class of fluctuating and driven physical systems that exhibit sustained currents. We find that the physical concept of a steady state, well known for systems at equilibrium, must be generalized to describe such systems. In these, the generalization of a steady state is associated with a stationary probability density of microstates and a deterministic dynamical system whose trajectories the system follows on average. These trajectories are a manifestation of nonstationary macroscopic currents observed in these systems. We determine precise conditions for the steady state to exist as well as the requirements for it to be stable. We illustrate this with some examples.