  Two statements by von Neumann and a thought-experiment by Peres prompts a
discussion on the notions of one-shot distinguishability, orthogonality,
semi-permeable diaphragm, and their thermodynamic implications. In the first
part of the paper, these concepts are defined and discussed, and it is
explained that one-shot distinguishability and orthogonality are contradictory
assumptions, from which one cannot rigorously draw any conclusion, concerning
e.g. violations of the second law of thermodynamics. In the second part, we
analyse what happens when these contradictory assumptions comes, instead, from
_two_ different observers, having different pieces of knowledge about a given
physical situation, and using incompatible density matrices to describe it.
