Nonequilibrium dynamics and umbrella sampling

In the past decade there has been considerable interest in nonequilibrium free energy theorems. These theorems show how the difference between the free energies of two equilibrium states of a system are related to distributions of work along nonequilibrium pathways. Here we significantly extend these theorems by relating the possibly inaccessible equilibrium average of any phase variable to the distribution of work along nonequilibrium paths. The result is elegant and analogous to the static umbrella sampling used with Monte Carlo simulations. The umbrella weight, which is related to the nonequilibrium work, is easy to obtain and efficient to compute. Furthermore, its average may be obtained from the existing nonequilibrium free energy theorem.