  For quantum mechanical systems, the microscopic state space is a Hilbert space. Dynamic evolution is generally through a unitary operator, but with doubly stochastic transitions if wavefunction collapse occurs. Volumes of regions of the state space are associated with the dimensionality of the smallest subspace containing the region, and an analogue of Liouville's Theorem holds for unitary evolution (doubly stochastic transitions may increase, but cannot decrease, this state space volume). For the most part there is little difference between the classical and quantum treatments of Szilard's engine and Landauer's principle and, unless stated otherwise, we will use the classical treatment. We will consider some of the suggested differences in Section 5.