Quantum entropy flows - updated

Non-equilibrium quantum thermodynamics is a quite new fields in physics that surprisingly left  less explored in the last century. Recently this field is becoming active both experimentally and theoretically. 

When interaction occurs between two systems there is a flow of some conserved quantities, such as electric charge, energy etc. between the two.  Shannon entropy (as well as its generalized Renyi entropy) is a conserved quantity in a world made of subsystems A and B.  Owing to this conservation there are finite flows of entropy between A and B.

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. 

Source: http://arxiv.org/abs/1408.3910

Rényi entropy flows from quantum heat engines
Mohammad H. Ansari, Yuli V. Nazarov

UPDATE:
An update is that paper has been published in Phys. Rev. B 91, 104303 - doi