  The quantum Szilard engine (QSZE) is a conceptual quantum engine for
understanding the fundamental physics of quantum thermodynamics and information
physics. We generalize the QSZE to an arbitrary spin case, i.e., a spin QSZE
(SQSZE), and we systematically study the basic physical properties of both
fermion and boson SQSZEs in a low-temperature approximation. We give the
analytic formulation of the total work. For the fermion SQSZE, the work might
be absorbed from the environment, and the change rate of the work with
temperature exhibits periodicity and even-odd oscillation, which is a
generalization of a spinless QSZE. It is interesting that the average absorbed
work oscillates regularly and periodically in a large-number limit, which
implies that the average absorbed work in a fermion SQSZE is neither an
intensive quantity nor an extensive quantity. The phase diagrams of both
fermion and boson SQSZEs give the SQSZE doing positive or negative work in the
parameter space of the temperature and the particle number of the system, but
they have different behaviors because the spin degrees of the fermion and the
boson play different roles in their configuration states and corresponding
statistical properties. The critical temperature of phase transition depends
sensitively on the particle number. By using Landauer's erasure principle, we
give the erasure work in a thermodynamic cycle, and we define an efficiency (we
refer to it as information-work efficiency) to measure the engine's ability of
utilizing information to extract work. We also give the conditions under which
the maximum extracted work and highest information-work efficiencies for
fermion and boson SQSZEs can be achieved.
