  We establish a finite-time external field-driven quantum tricycle model.
Within the framework of slow driving perturbation, the perturbation expansion
of heat in powers of time can be derived during the heat exchange processes.
Employing the method of Lagrange multiplier, we optimize the cooling
performance of the tricycle by considering the cooling rate and the figure of
merit, which is the product of the coefficient of performance and cooling rate,
as objective functions. Our findings reveal the optimal operating region of the
tricycle, shedding light on its efficient performance.
