  In this work, we introduce an information-theoretic approach for considering
changes in dynamics of finitely dimensional open quantum systems governed by
master equations. This experimentally motivated approach arises from
considering how the averages of system observables change with time and
quantifies how non-stationary the system is during a given time regime. By
drawing an analogy with the exponential decay, we are able to further
investigate regimes when such changes are negligible according to the
logarithmic scale of time, and thus the system is approximately stationary.
While this is always the case within the initial and final regimes of the
dynamics, with the system respectively approximated by its initial and
asymptotic states, we show that a distinct regime of approximate stationarity
may arise. In turn, we establish a quantitative description of the phenomenon
of metastability in open quantum systems. The initial relaxation occurring
before the corresponding metastable regime and of the long-time dynamics taking
place afterwards are also characterised. Furthermore, we explain how
metastability relates to the separation in the real part of the master equation
spectrum and connect our approach to the spectral theory of metastability,
clarifying when the latter follows. All of our general results directly
translate to Markovian dynamics of classical stochastic systems.
