The Free Action of Nonequilibrium Dynamics

In general nonequilibrium steady states, directly replacing the canonical ensemble by the nonequilibrium invariant distribution yields a free energy function that is insufficient in characterizing the dynamical landscape. We address the problem by defining the free action, which is like a free energy on path space. Through a representative example, we demonstrate the conceptual and practical usefulness of the free action for quantifying the dynamics of nonequilibrium steady states, including those exhibiting phase transitions.