Computation of free energy differences through nonequilibrium stochastic dynamics: the reaction coordinate case

The computation of free energy differences through an exponential weighting of out of equilibrium paths (known as the Jarzynski equality) is often used for transitions between states described by an external parameter $\lambda$ in the Hamiltonian. We present here an extension to transitions between states defined by different values of some reaction coordinate, using a projected Brownian dynamics. In contrast with other approaches, we use a projection rather than a constraining potential to let the constraints associated with the reaction coordinate evolve. We show how to use the Lagrange multipliers associated with these constraints to compute the work associated with a given trajectory. Appropriate discretizations are proposed. Some numerical results demonstrate the applicability of the method for the computation of free energy difference profiles.