  A deeper understanding of the differences between quantum and classical
dynamics promises great potential for emerging technologies. Nevertheless, some
aspects remain poorly understood, particularly concerning the role of quantum
coherence in open quantum systems. On the one hand, coherence leads to
entanglement and even nonlocality. On the other, it may lead to a suppression
of fluctuations, causing violations of thermo-kinetic uncertainty relations
(TUR and KUR) that are valid for classical processes. These represent two
different manifestations of coherence, one depending only on the state of the
system (static) and one depending on two-time correlation functions
(dynamical). Here we employ these manifestations of coherence to determine when
mesoscopic quantum transport can be captured by a classical model based on
stochastic jumps, and when such a model breaks down, implying nonclassical
behavior. To this end, we focus on a minimal model of a double quantum dot
coupled to two thermal reservoirs. In this system, quantum tunneling induces
Rabi oscillations and results in both entanglement and nonlocality, as well as
TUR and KUR violations. These effects, which describe the breakdown of a
classical description, are accompanied by a peak in coherence. Our results
provide guiding principles for the design of out-of-equilibrium devices that
exhibit nonclassical behavior.
