On the Relative Merits of Equilibrium and Non-Equilibrium Simulations for the Estimation of Free-Energy Differences

The possibility of estimating equilibrium free-energy profiles from multiple non-equilibrium simulations using the fluctuation-dissipation theory or the relation proposed by Jarzynski has attracted much attention. Although the Jarzynski estimator has poor convergence properties for simulations far from equilibrium, corrections have been derived for cases in which the work is Gaussian distributed. Here, we examine the utility of corrections proposed by Gore and collaborators using a simple dissipative system as a test case. The system consists of a single methane-like particle in explicit water. The Jarzynski equality is used to estimate the change in free energy associated with pulling the methane particle a distance of 3.9 nm at rates ranging from similar to 0.1 to 100 ms(-1). It is shown that although the corrections proposed by Gore and collaborators have excellent numerical performance, the profiles still converge slowly. Even when the corrections are applied in an ideal case where the work distribution is necessarily Gaussian, performing simulations under quasi-equilibrium conditions is still most efficient. Furthermore, it is shown that even for a single methane molecule in water, pulling rates as low as 1 ms(-1) can be problematic. The implications of this finding for studies in which small molecules or even large biomolecules are pulled through inhomogeneous environments at similar pulling rates are discussed.