  Quantum decoherence is seen as an undesired source of irreversibility that
destroys quantum resources. Quantum coherences seem to be a property that
vanishes at thermodynamic equilibrium. Away from equilibrium, quantum
coherences challenge the classical notions of a thermodynamic bath in a Carnot
engines, affect the efficiency of quantum transport, lead to violations of
Fourier's law, and can be used to dynamically control the temperature of a
state. However, the role of quantum coherence in thermodynamics is not fully
understood. Here we show that the relative entropy of a state with quantum
coherence with respect to its decohered state captures its deviation from
thermodynamic equilibrium. As a result, changes in quantum coherence can lead
to a heat flow with no associated temperature, and affect the entropy
production rate. From this, we derive a quantum version of the Onsager
reciprocal relations that shows that there is a reciprocal relation between
thermodynamic forces from coherence and quantum transport. Quantum decoherence
can be useful and offers new possibilities of thermodynamic control for quantum
transport.
