  Quantum measurement of a system can change its mean energy, as well as
entropy. A selective measurement (classical or quantum) can be used as a
"Maxwell's demon" to power a single-temperature heat engine, by decreasing the
entropy. Quantum mechanically, so can a non-selective measurement, despite
increasing the entropy of a thermal state. The maximal amount of work
extractable following the measurement is given by the change in free energy:
$W_{max}^{(non-)sel.}=\Delta E_{meas}-T_{Bath}\Delta S_{meas}^{(non-)sel.}$.
This follows from the "generalized 2nd law for nonequilibrium initial state"
[Hasegawa et. al, PLA (2010)], of which an elementary reduction to the standard
law is given here. It is shown that $W_{max}^{sel.}-W_{max}^{non-sel.}$ equals
the work required to reset the memory of the measuring device, and that no such
resetting is needed in the non-selective case. Consequently, a single-bath
engine powered by either kind of measurement works at a net loss of
$T_{Bath}\Delta S_{meas}^{non-sel}$ per cycle. By replacing the measurement by
a reversible "premeasurement" and allowing a work source to couple to the
system and memory, the cycle can be made completely reversible.
