Equilibrium free energies from nonequilibrium simulations: Improving convergence by reducing dissipation

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## Abstract

The estimation of equilibrium free energy differences is an important problem in computational thermodynamics, with applications to studies of ligand binding, phase coexistence and phase equilibrium, solvation of small molecules, and computational drug design, among others. Recent advances in nonequilibrium statistical mechanics, in particular the discovery of exact nonequilibrium work fluctuation relations, have made it possible to estimate equilibrium free energy differences from simulations of nonequilibrium processes in which a system of interest is driven irreversibly between two equilibrium states.

Estimates of the free energy difference obtained from processes in which the system is driven far from equilibrium often suffer from poor convergence as a consequence of the dissipation that typically accompanies such processes. This thesis is concerned with this problem of poor convergence, and studies methods to improve the efficiency of such estimators. A central theoretical result that guides the development of these methods is a quantitative connection between dissipation and the extent to which the system ``lags'' behind the actual equilibrium state, at any point in time of the nonequilibrium process.

The first strategy involves generating `escorted" trajectories in the nonequilibrium simulation by introducing artificial terms that directly couple the evolution of the system to changes in the external parameter. Estimators for the free energy difference in terms of these artificial trajectories are developed and it is shown that whenever the artificial dynamics manage to reduce the lag, the convergence of the free energy estimate is improved. We demonstrate the effectiveness of this method on a few model systems. In particular, we demonstrate how this method can be used to obtain efficient estimates of solvation free energies of model hard sphere solutes in water and other solvents. In the second strategy,`

protocol postprocessing", the trajectories normally generated in the course of a nonequilibrium simulation are used to construct estimators of the free energy difference that converge faster than the usual estimators. Again, the connection between dissipation and lag guides the development of this method. The effectiveness of this strategy is also demonstrated on a few model systems.