Nonequilibrium work theorems applied to transitions between configurational domains

Abstract

A nonequilibrium simulation scheme extending the field of applicability of the Jarzynski equality (Jarzynski 1997 Phys. Rev. Lett. 78 2690) and Crooks fluctuation theorem (Crooks 2000 Phys. Rev. E 61 2361) is presented. The algorithm is based on steps, consisting of transition kernels, alternated to relaxation kernels, that drive the system from an initial to a final configurational domain within the space of the (externally controlled) collective coordinates. This allows the producing of nonequilibrium paths connecting two states with arbitrary shape and size in the space of the collective coordinates, giving access to their free energy difference. The method can be viewed as a generalization of the steered molecular dynamics, a technique commonly applied in simulation to calculate the potentials of mean force along an established monodimensional path in the space of the collective coordinates. A numerical validation of the method is provided by estimating the free energy differences in two model systems featured by a double-well potential. The outcomes are compared to those obtained from standard steered molecular dynamics simulations.