Thermodynamic and quantum entropy gain of frame averaging

We are discussing a universal non-unitary map M subsequent to a generic unitary map U, whose von Neumann entropy gain coincides with the calculated thermodynamic entropy production. For many-body quantum reservoirs we prove that M can be the averaging over all translations of the spatial frame. Assuming the coincidence of microscopic and macroscopic entropy productions leads to a novel equation between entropy gain of frame averaging and relative entropy. Our map M turns out to coincide with the older one called twirl, used recently in the theory of quantum reference frames. Related results to ours have been obtained and we discuss some of them briefly. Possible relevance of frame averaging (twirling) for real world irreversibility is mentioned.