  The free-energy difference $\Delta F$ 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 $\Delta F$ estimates that are orders of
magnitude lower in mean squared error than the generic linear interpolation
protocol with which it is initialized.
