Equilibrium time correlation functions from irreversible transformations in trajectory space

We present a new identity for the statistical mechanics of trajectories, showing that a distribution of irreversible transformations between ensembles of trajectories is sufficient to determine equilibrium time correlation functions. This general and exact result extends to the dynamical realm recently derived connections between thermodynamic free energies and statistics out of equilibrium. We focus on the specific application to population correlation functions characterizing chemical kinetics. In this context we use the identity to compute reaction rate constants through appropriate averaging of an effective work to switch from nonreactive to reactive trajectory ensembles. There is in principle no restriction on how quickly this switching of ensembles is performed. We demonstrate the practicality of such a calculation for a model isomerization in dense solvent.