  One of the stunning consequences of quantum correlations in thermodynamics is
the reversal of the arrow of time, recently shown experimentally in [K.
Micadei, et al., Nat. Commun. 10:2456 (2019)], and manifesting itself by a
reversal of the heat flow (from the cold system to the hot one). Here, we show
that contrary to what could have been expected, heat flow reversal can happen
without reversal of the arrow of time. Moreover, contrasting with previous
studies, no initial correlations between system and bath is required. Instead,
the heat flow reversal only relies on internal quantum coherences or
correlations, which provides practical advantages over previous schemes: one
does not need to have access to the bath in order to reverse the heat flow. The
underlying mechanism is explained and shown to stem from the collective
system-bath coupling and the impact of non-energetic coherences (coherences
between degenerate energy levels) on apparent temperatures. The phenomenon is
first uncovered in a broad framework valid for diverse quantum systems
containing energy degeneracy. By the end of the paper, aiming at experimental
realisations, more quantitative results are provided for a pair of two-level
systems. Finally, as a curiosity, we mention that our scheme can be adapted as
a correlations-to-energy converter, which have the particularity to be able to
operate at constant entropy, similarly to ideal work sources.
