  Realistic models of biological processes typically involve interacting
components on multiple scales, driven by changing environment and inherent
stochasticity. Such models are often analytically and numerically intractable.
We revisit a dynamic maximum entropy method that combines a static maximum
entropy and a quasi-stationary approximation. This allows us to reduce
stochastic non-equilibrium dynamics expressed by the Fokker-Planck equation to
a simpler low-dimensional deterministic dynamics, without the need to track
microscopic details. Although the method has been previously applied to a few
(rather complicated) applications in population genetics, our main goal here is
to explain and to better understand how the method works. We demonstrate the
usefulness of the method for two widely studied stochastic problems,
highlighting its accuracy in capturing important macroscopic quantities even in
rapidly changing non-stationary conditions. For the Ornstein-Uhlenbeck process,
the method recovers the exact dynamics whilst for a stochastic island model
with migration from other habitats, the approximation retains high macroscopic
accuracy under a wide range of scenarios for a dynamic environment.
