  We study the efficiency of a simple quantum dot heat engine at maximum power.
In contrast to the quasi-statically operated Carnot engine whose efficiency
reaches the theoretical maximum, recent research on more realistic engines
operated in a finite time has revealed other classes of efficiencies such as
the Curzon-Ahlborn efficiency maximizing the power. Such a power-maximizing
efficiency has been argued to be always the half of the maximum efficiency up
to the linear order near equilibrium under the tight-coupling condition between
thermodynamic fluxes. We show, however, that this universality may break down
for the quantum dot heat engine, depending on the constraint imposed on the
engine control parameters (local optimization), even though the tight-coupling
condition remains satisfied.It is shown that this deviation is critically
related to the applicability of the linear irreversible thermodynamics.
