  We construct an example of heat engine whose efficiency at maximum power
breaks down the previously derived bounds in the linear response regime. Such
example takes a classical harmonic oscillator as the working substance
undergoing a finite-time Otto cycle. Using a specific kind of shortcut to
adiabaticity, valid only in the linear response regime, quasistatic work is
performed at arbitrarily short times. The cycle duration is then reduced to the
sum of relaxation times during the thermalization strokes exclusively. Thus,
power is maximum since the work is maximum (quasistatic work) and the cycle
duration is minimum. Efficiency at maximum power can be made arbitrarily close
to Carnot efficiency with an appropriate choice of the ratio between the
temperatures of the two heat baths.
