Fluctuations of quantum currents and unravelings of master equations

The very notion of a current fluctuation is problematic in the quantum context. We study that problem in the context of nonequilibrium statistical mechanics, both in a microscopic setup and in a Markovian model. Our answer is based on a rigorous result that relates the weak coupling limit of fluctuations of reservoir observables under a global unitary evolution with the statistics of the so-called quantum trajectories. These quantum trajectories are frequently considered in the context of quantum optics, but they remain useful for more general nonequilibrium systems. In contrast with the approaches found in the literature, we do not assume that the system is continuously monitored. Instead, our starting point is a relatively realistic unitary dynamics of the full system.