Time-asymmetric fluctuation theorem and efficient free-energy estimation

Abstract

The free-energy difference $\mathrm{\Delta }F$ between two high-dimensional systems is notoriously difficult to compute but very important for many applications such as drug discovery. We demonstrate that an unconventional definition of work introduced by Vaikuntanathan and Jarzynski (2008) satisfies a microscopic fluctuation theorem that relates path ensembles that are driven by protocols unequal under time reversal. It has been shown before that counterdiabatic protocols—those having additional forcing that enforces the system to remain in instantaneous equilibrium, also known as escorted dynamics or engineered swift equilibration—yield zero-variance work measurements for this definition. We show that this time-asymmetric microscopic fluctuation theorem can be exploited for efficient free-energy estimation by developing a simple (i.e., neural-network free) and efficient adaptive time-asymmetric protocol optimization algorithm that yields $\mathrm{\Delta }F$ estimates that are orders of magnitude lower in mean squared error than the generic linear interpolation protocol with which it is initialized.