  The efficiency of cyclic heat engines is limited by the Carnot bound. This
bound follows from the second law of thermodynamics and is attained by engines
that operate between two thermal baths under the reversibility condition
whereby the total entropy does not increase. By contrast, the efficiency of
engines powered by quantum non-thermal baths has been claimed to surpass the
thermodynamic Carnot bound. The key to understanding the performance of such
engines is a proper division of the energy supplied by the bath to the system
into heat and work, depending on the associated change in the system entropy
and ergotropy. Due to their hybrid character, the efficiency bound for quantum
engines powered by a non-thermal bath does not solely follow from the laws of
thermodynamics. Hence, the thermodynamic Carnot bound is inapplicable to such
hybrid engines. Yet, they do not violate the principles of thermodynamics.
  An alternative means of boosting machine performance is the concept of
heat-to-work conversion catalysis by quantum non-linear (squeezed) pumping of
the piston mode. This enhancement is due to the increased ability of the
squeezed piston to store ergotropy. Since the catalyzed machine is fueled by
thermal baths, it adheres to the Carnot bound.
  We conclude by arguing that it is not quantumness per se that improves the
machine performance, but rather the properties of the baths, the working fluid
and the piston that boost the ergotropy and minimize the wasted heat in both
the input and the output.
