  We define the entropy operator as the negative of the logarithm of the
density matrix, give a prescription for extracting its thermodynamically
measurable part, and discuss its dynamics. For an isolated system we derive the
first, second and third laws of thermodynamics. For weakly-coupled subsystems
of an isolated system, an expression for the long time limit of the expectation
value of the rate of change of the thermodynamically measurable part of the
entropy operator is derived and interpreted in terms of entropy production and
entropy transport terms. The interpretation is justified by comparison to the
known expression for the entropy production in an aged classical Markovian
system with Gaussian fluctuations and by a calculation of the current-induced
entropy production in a conductor with electron-phonon scattering.
