Thermodynamic Uncertainty Relation for General Open Quantum Systems

We derive a thermodynamic uncertainty relation for general open quantum dynamics, described by joint unitary evolution on composite system comprising and an environment. By measuring the environmental state after system-environment interaction, we bound counting observables in environment survival activity, which reduces to dynamical activity classical Markov processes. Remarkably, derived herein holds systems with any observable initial state. Therefore, our is satisfied processes arbitrary time-dependent transition rates states. apply continuous measurement walk find that nature of can enhance precision. Moreover, make lower arbitrarily small employing appropriate measurement.