Power-Efficiency Constraint for Chemical Motors

The mechanical movement driven by chemical gradients provides the primordial energy for biological functions. Its thermodynamic properties remains inclusive, especially for a dynamical change of energy demand in biological systems. In this article, we obtain a constraint relation between the changing output power and the conversion efficiency for a chemically fuelled rotary motor analogous to the $\mathrm{F}_{0}$-motor of ATPase. We find the efficiency at maximum power is half of the maximum quasi-static efficiency. These findings shall aid in the understanding of natural chemical engines and inspire the manual design and control of chemically fuelled microscale engines.