  The entropy production in dissipative processes is the essence of the arrow
of time and the second law of thermodynamics. For dissipation of quantum
systems, it was recently shown that the entropy production contains indeed two
contributions: a classical one and a quantum one. Here we show that for
degenerate (or near-degenerate) quantum systems there are additional quantum
contributions which, remarkably, can become negative. Furthermore, such
negative contributions are related to significant changes in the ongoing
thermodynamics. This includes phenomena such as generation of coherences
between degenerate energy levels (called horizontal coherences), alteration of
energy exchanges and, last but not least, reversal of the natural convergence
of the populations toward the thermal equilibrium state. Going further, we
establish a complementarity relation between horizontal coherences and
population convergence, particularly enlightening for understanding heat flow
reversals. Conservation laws of the different types of coherences are derived.
Some consequences for thermal machines and resource theory of coherence are
suggested.
