For the first time we present a consistent derivation of the flows of Shannon and Renyi entropies for a generic quantum heat engine to a probe environment kept in thermal equilibrium. The flows consist of heat flow and fictitious dissipation originating from quantum coherence.
Rényi entropy flows from quantum heat engines
Mohammad H. Ansari, Yuli V. Nazarov
An update is that paper has been published in Phys. Rev. B 91, 104303 - doi