  We study the role of quantum statistics in the performance of Otto cycles.
First, we show analytically that the work distributions for bosonic and
fermionic working fluids are identical for cycles driven by harmonic trapping
potentials. Subsequently, in the case of non-harmonic potentials, we find that
the interplay between different energy level spacings and particle statistics
strongly affects the performances of the engine cycle. To demonstrate this, we
examine three trapping potentials which induce different (single particle)
energy level spacings: monotonically decreasing with the level number,
monotonically increasing, and the case in which the level spacing does not vary
monotonically.
