Rare-event sampling for driven inertial systems via the nonequilibrium distribution function

Recently substantial generalizations have been made to the Yamada-Kawasaki type nonlinear response theory formalism for deterministic dynamics. These provide opportunities to develop new importance sampling techniques against known distribution functions. We exploit this to develop a method of calculating nonequilibrium rate constants across a large free energy barrier, allowing molecular simulations to access far greater time scales. In contrast to existing stochastic methods, we do not merely follow the dynamics forward in time, allowing systems governed by inertial equations of motion to be usefully addressed. We further generalize the Yamada-Kawasaki type formalism to the case of stochastic equations of motion and the resulting nonequilibrium importance sampling method follows straight forwardly. We quantitatively test the method on stochastic and deterministic models, specifically chosen to allow a comparison with reliable, independently obtained data. To do this we consider oscillators in a one-dimensional double well potential. Either side of the well is separated by an energy barrier and the oscillator is driven away from equilibrium by a position dependent temperature profile. The energy barrier is chosen to be low enough that we can still solve the system computationally by brute force. We demonstrate that the results of our method are consistent with those from the brute force simulations to very high accuracy. We also show how our method is more than two orders of magnitude more efficient for the given example than forward flux sampling.