  Biological motors, as counterpart of heat engines, are driven by a chemical
gradient to output mechanical work and play critical roles in biological
functions, such as the ATP synthesis. Its thermodynamic efficiency, along with
power, are two vital criteria for evaluating the performance of these motors.
In this letter, we investigate a model of a microscopic chemical engine and
assess the constraint relation between power and efficiency for the cycle with
finite operation time. Our model demonstrates a general constraint relation
between power and efficiency, and predicts that the efficiency at maximum power
in the large friction regime is half of the maximum quasi-static efficiency,
i.e., 1/2. These findings shall provide new direction to optimize the operation
of microscopic biological motors.
