  The Kullback-Leibler inequality is a way of comparing any two density
matrices. A technique to set up the density matrix for a physical system is to
use the maximum entropy principle, given the entropy as a functional of the
density matrix, subject to known constraints. In conjunction with the master
equation for the density matrix, these two ingredients allow us to formulate
the second law of thermodynamics in its widest possible setting. Thus problems
arising in both quantum statistical mechanics and quantum information can be
handled. Aspects of thermodynamic concepts such as the Carnot cycle will be
discussed. A model is examined to elucidate the role of entanglement in the
Landauer erasure problem.
