  Single-molecule experiments have found near-perfect thermodynamic efficiency
in the rotary motor F1-ATP synthase. To help elucidate the principles
underlying nonequilibrium energetic efficiency in such stochastic machines, we
investigate driving protocols that minimize dissipation near equilibrium in a
simple model rotary mechanochemical motor, as determined by a generalized
friction coefficient. Our simple model has a periodic friction coefficient that
peaks near system energy barriers. This implies a minimum-dissipation protocol
that proceeds rapidly when the system is overwhelmingly in a single macrostate,
but slows significantly near energy barriers, thereby harnessing thermal
fluctuations to kick the system over energy barriers with minimal work input.
This model also manifests a phenomenon not seen in otherwise similar
non-periodic systems: sufficiently fast protocols can effectively lap the
system. While this leads to a non-trivial tradeoff between accuracy of driving
and energetic cost, we find that our designed protocols out-perform naive
protocols.
