  We investigate a heat engine with a finite-length Kitaev chain in an ideal
Otto cycle. It is found that the critical point of the topological phase
transition coincides with the maxima of the efficiency and work output of the
total Otto engine. Finite-size effects are taken into account using the method
of Hill's nanothermodynamics, as well as using the method of
temperature-dependent energy levels. We identify the bulk and boundary thermal
cycles of the Kitaev chain engine and find that they are non-ideal Otto cycles.
The physics of deviation from ideal Otto cycle is identified as a finite size
effect, which we dub as "internal geometric friction", leading to heat transfer
from the bulk to the boundary during adiabatic transformation of the whole
system. Besides, we determine the regimes allowing for independently running an
ideal Otto refrigerator at the boundary and an ideal Otto engines in the bulk
and in the whole system. Furthermore, we show that the first-order phase
transition in the boundary and the second-order phase transition in the bulk
can be identified through their respective contributions to the engine work
output.
