  The nonequilibrium fluctuation theorems have paved the way for estimating
equilibrium thermodynamic properties, such as free energy differences, using
trajectories from driven nonequilibrium processes. While many statistical
estimators may be derived from these identities, some are more efficient than
others. It has recently been suggested that trajectories sampled using a
particular time-dependent protocol for perturbing the Hamiltonian may be
analyzed with another one. Choosing an analysis protocol based on the
nonequilibrium density was empirically demonstrated to reduce the variance and
bias of free energy estimates. Here, we present an alternate mathematical
formalism for protocol postprocessing based on the Feynmac-Kac theorem. The
estimator that results from this formalism is demonstrated on a few
low-dimensional model systems. It is found to have reduced bias compared to
both the standard form of Jarzynski's equality and the previous protocol
postprocessing formalism.
