  In this paper, we analyze the operation of an Otto cycle heat machine driven
by a non-interacting two-dimensional electron gas on a twisted geometry. We
show that due to both the energy quantization on this structure and the
adiabatic transformation of the number of complete twists per unit length of a
helicoid, the machine performance in terms of output work, efficiency, and
operation mode can be altered. We consider the deformations as in a spring,
which is either compressed or stretched from its resting position. The
realization of classically inconceivable Otto machines with an incompressible
sample can be realized as well. The energy-level spacing of the system is the
quantity that is being either compressed or stretched. These features are due
to the existence of an effective geometry-induced quantum potential which is of
pure quantum-mechanical origin.
