Power-Efficiency Constraint for Chemical Motors

Chemical gradients provide the primordial energy for biological functions by driving the mechanical movement of microscopic engines. Their thermodynamic properties remain elusive, especially concerning the dynamic change in energy demand in biological systems. In this article, we derive a constraint relation between the output power and the conversion efficiency for a chemically fueled steady-state rotary motor analogous to the $\mathrm{F}_o$ motor of ATPase. We find that 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 fueled microscale engines.