Numerical comparison of a constrained path ensemble and a driven quasisteady state

We investigate the correspondence between a nonequilibrium ensemble defined via the distribution of phase-space paths of a Hamiltonian system and a system driven into a steady state by nonequilibrium boundary conditions. To discover whether the nonequilibrium path ensemble adequately describes the physics of a driven system, we measure transition rates in a simple one-dimensional model of rotors with Newtonian dynamics and purely conservative interactions. We compare those rates with known properties of the nonequilibrium path ensemble. In doing so, we establish effective protocols for the analysis of transition rates in nonequilibrium quasisteady states. Transition rates between potential wells and also between phase-space elements are studied and found to exhibit distinct properties, the more coarse-grained potential wells being effectively further from equilibrium. In all cases the results from the boundary-driven system are close to the path-ensemble predictions, but the question of equivalence of the two remains open.