  Experiments often probe observables that correspond to low-dimensional
projections of highdimensional dynamics. In such situations distinct
microscopic configurations become lumped into the same observable state. It is
well known that correlations between the observable and the hidden degrees of
freedom give rise to memory effects. However, how and under which conditions
these correlations emerge remains poorly understood. Here we shed light on two
fundamentally different scenarios of the emergence of memory in minimal
stationary systems, where observed and hidden degrees of freedom evolve either
cooperatively or are coupled by a hidden non-equilibrium current. In the
reversible setting strongest memory manifests when the time-scales of hidden
and observed dynamics overlap, whereas, strikingly, in the driven setting
maximal memory emerges under a clear time-scale separation. Our results hint at
the possibility of fundamental differences in the way memory emerges in
equilibrium versus driven systems that may be utilized as a "diagnostic" of the
underlying hidden transport mechanism.
