  Entropy is one of the central quantities in thermodynamics, whose flow
between two systems determines the statistics of energy transfers. In quantum
systems entropy is non-linear in density matrix whose time evolution is
cumbersome. Using recent developments in the Keldysh formalism for the
evolution of nonlinear quantum information measures (Phys. Rev. B 91, 174307
(2015)), we study the flow of von Neumann and Renyi entropies in a generic
four-level quantum system that is weakly coupled to equilibrium heat engines.
We show that noise-induced coherence has significant influence on the entropy
flow of the quantum heat engine. We determine analytical optimization of
couplings for the purpose of designing optimal artificial energy transfer
systems.
