  Understanding out-of-equilibrium quantum dynamics is a critical outstanding
problem, with key questions regarding characterizing adiabaticity for
applications in quantum technologies. We show how the metric-space approach to
quantum mechanics naturally characterizes regimes of quantum dynamics, and
provides an appealingly visual tool for assessing their degree of adiabaticity.
Further, the dynamic trajectories of quantum systems in metric space suggest a
lack of "ergodicity", thus providing a better understanding of the fundamental
one-to-one mapping between densities and wavefunctions.
