  In this paper, we analyze the total work extracted and the efficiency of the
magnetic Otto cycle in its classic and quantum versions. As a general result,
we found that the work and efficiency of the classical engine is always greater
than or equal to that of its quantum counterpart independent of the working
substance. In the classical case, this is due to the fact that the working
substance is always in thermodynamic equilibrium at each point of the cycle,
maximizing the energy extracted in the adiabatic paths. We apply this analysis
to the case of a two-level system, finding that the work and efficiency in
Otto's quantum and classical cycle are identical, regardless of the working
substance, and we obtain similar results for a multilevel system where a linear
relationship between the spectrum of energies of the working substance and the
external magnetic field is fulfilled. Finally, we show an example of a
three-level system in which we compare two zones in the entropy, temperature
and magnetic field diagram to find which is the most efficient when performing
a thermodynamic cycle. This work provides a practical way to look for
temperature and magnetic field zones in the entropy diagram that can maximize
the power extracted from Otto's magnetic engine.

Statistical Mechanics;Other Condensed Matter