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Experiments often probe observables that correspond to low-dimensionalprojections of highdimensional dynamics. In such situations distinctmicroscopic configurations become lumped into the same observable state. It iswell known that correlations between the observable and the hidden degrees offreedom give rise to memory effects. However, how and under which conditionsthese correlations emerge remains poorly understood. Here we shed light on twofundamentally different scenarios of the emergence of memory in minimalstationary systems, where observed and hidden degrees of freedom evolve eithercooperatively or are coupled by a hidden non-equilibrium current. In thereversible setting strongest memory manifests when the time-scales of hiddenand observed dynamics overlap, whereas, strikingly, in the driven settingmaximal memory emerges under a clear time-scale separation. Our results hint atthe possibility of fundamental differences in the way memory emerges inequilibrium versus driven systems that may be utilized as a "diagnostic" of theunderlying hidden transport mechanism.

On the emergence of memory in equilibrium versus non-equilibrium systems