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In classical thermodynamics energy always flows from the hotter system to thecolder one. However, if these systems are initially correlated, the energy flowcan reverse, making the cold system colder and the hot system hotter. Thisintriguing phenomenon is called ``anomalous energy flow'' and shows theimportance of initial correlations in determining physical properties ofthermodynamic systems. Here we investigate the fundamental limits of thiseffect. Specifically, we find the optimal amount of energy that can betransferred between quantum systems under closed and reversible dynamics, whichthen allows us to characterize the anomalous energy flow. We then explore amore general scenario where the energy flow is mediated by an ancillary quantumsystem that acts as a catalyst. We show that this approach allows forexploiting previously inaccessible types of correlations, ultimately resultingin an energy transfer that surpasses our fundamental bound. To demonstratethese findings, we use a well-studied quantum optics setup involving two atomscoupled to an optical cavity.

Fundamental limits on anomalous energy flows in correlated quantum systems