  Recent research on the thermodynamic arrow of time, at the microscopic scale,
has questioned the universality of its direction. Theoretical studies showed
that quantum correlations can be used to revert the natural heat flow (from the
hot body to the cold one), posing an apparent challenge to the second law of
thermodynamics. Such an "anomalous" heat current was observed in a recent
experiment (arXiv:1711.03323), by employing two spin systems initially quantum
correlated. Nevertheless, the precise relationship between this intriguing
phenomenon and the initial conditions that allow it is not fully evident. Here,
we address energy transfer in a wider perspective, identifying a nonclassical
contribution that applies to the reversion of the heat flow as well as to more
general forms of energy exchange. We derive three theorems that describe the
energy transfer between two microscopic systems, for arbitrary initial
bipartite states. Using these theorems, we obtain an analytical bound showing
that certain type of quantum coherence can optimize such a process,
outperforming incoherent states. This genuine quantum advantage is corroborated
through a characterization of the energy transfer between two qubits. For this
system, it is shown that a large enough amount of coherence is necessary and
sufficient to revert the thermodynamic arrow of time. As a second crucial
consequence of the presented theorems, we introduce a class of nonequilibrium
states that only allow unidirectional energy flow. In this way, we broaden the
set where the standard Clausius statement of the second law applies.
