  We study the physical mechanism of Maxwell's Demon (MD) helping to do extra
work in thermodynamic cycles, by describing measurement of position, insertion
of wall and information erasing of MD in a quantum mechanical fashion. The heat
engine is exemplified with one molecule confined in an infinitely deep square
potential inserted with a movable solid wall, while the MD is modeled as a
two-level system (TLS) for measuring and controlling the motion of the
molecule. It is discovered that the the MD with quantum coherence or on a lower
temperature than that of the heat bath of the particle would enhance the
ability of the whole work substance formed by the system plus the MD to do work
outside. This observation reveals that the role of the MD essentially is to
drive the whole work substance being off equilibrium, or equivalently working
with an effective temperature difference. The elaborate studies with this model
explicitly reveal the effect of finite size off the classical limit or
thermodynamic limit, which contradicts the common sense on Szilard heat engine
(SHE). The quantum SHE's efficiency is evaluated in detail to prove the
validity of second law of thermodynamics.
