Quantum Nonequilibrium Statistical Mechanics Meets the Measurement Problem

We present a complete theory of experimental measurement for heat and work on small nonequilibrium quantum systems under strong environmental coupling. It is consistent with the usual laws of thermodynamics at all temperatures, while only operating on ancilla that interacted with the system at some time. We show that the back-action of measurement must be counted as work rather than heat to satisfy the second law, and that this back-action strictly prevents reversible conversion of heat and entropy in the quantum setting. Our total entropy production is a lower bound on weak coupling, quantum jump / unravelling, and transition-probability based definitions, which appear as particular limits of the present model. Two interesting consequences of the theory are that systems actively interacting with a real environment have a minimum achievable temperature irrespective of the environmental temperature, and that it is impossible to apply traditional fluctuation relations in the presence of back-action. The phenomenon of minimum temperature offers a novel explanation of recent experiments aimed at testing fluctuation theorems in the quantum realm and places a fundamental purity limit on quantum computers.