  The hypothetical possibility of distinguishing preparations described by
non-orthogonal density matrices does not necessarily imply a violation of the
second law of thermodynamics, as was instead stated by von Neumann. On the
other hand, such a possibility would surely mean that the particular
density-matrix space (and related Hilbert space) adopted would not be adequate
to describe the hypothetical new experimental facts. These points are shown by
making clear the distinction between physical preparations and the density
matrices which represent them, and then comparing a "quantum" thermodynamic
analysis given by Peres with a "classical" one given by Jaynes.
