Non-orthogonality of statistical matrices and violations of the second law of thermodynamics

Vladislav Čápek, Jiří Bok

PierGianLuca Porta Mana

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.

Miodrag L. Kulić, Davidović-Ristovski, G. S., Ristovski, Lj. M.

PierGianLuca Porta Mana, A. Maansson, Gunnar G. Bjork

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.

Jurij Avsec, Milan Marčič

Wojciech H. Zurek

The second law of thermodynamics imposes severe constraints on the formal structure of quantum theory. In particular, that law would be violated if it were possible to distinguish non-orthogonal states or if SchrOdinger's equation were nonlinear.