High-Efficiency Free Energy Estimates Based on Variational Shortcuts to Isothermality

The mean work in an isothermal process is widely acknowledged as an accurate estimator of the free energy difference, but the high time cost limits its practical applications. Here, enlightened by the Gauss principle of least constraint, we develop a variational method for approximately accelerating isothermal processes and thereby estimating the free energy difference by using an equality between the free energy difference and the mean work related to the original Hamiltonian. The saddle-point approximation is applied to calculate the nonequilibrium "constraint" of the accelerated isothermal process. The simulations confirm that our method can efficiently estimate the free energy difference with high accuracy. Especially during fast driving processes, where dissipation is expected to be high, the estimates given by our method largely outperforms the estimates given by the mean work and the Jarzynski equality.