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Recently discovered identities in statistical mechanics have enabled thecalculation of equilibrium ensemble averages from realizations of drivennonequilibrium processes, including single-molecule pulling experiments andanalogous computer simulations. Challenges in collecting large data setsmotivate the pursuit of efficient statistical estimators that maximize use ofavailable information. Along these lines, Hummer and Szabo developed anestimator that combines data from multiple time slices along a drivennonequilibrium process to compute the potential of mean force. Here, wegeneralize their approach, pooling information from multiple time slices toestimate arbitrary equilibrium expectations. Our expression may be combinedwith estimators of path-ensemble averages, including existing optimalestimators that use data collected by unidirectional and bidirectionalprotocols. We demonstrate the estimator by calculating free energies, momentsof the polymer extension, and the metric tensor for thermodynamic length in amodel single-molecule pulling experiment. Compared to estimators that only useindividual time slices, our multiple time-slice estimators yield substantiallysmoother estimates and achieve lower variance for higher-order moments.

journal of chemical physics online/the journal of chemical physics/journal of chemical physics

Estimating equilibrium ensemble averages using multiple time slices from  driven nonequilibrium processes: theory and application to free energies,  moments, and thermodynamic length in single-molecule pulling experiments