Heat engine entropy flow controlled by entanglement

We calculate the entropy flow of a two-qubit heat engine and its dependence on entanglement between the qubits. Each qubit is weakly coupled to a heat reservoir, each at a different temperature and the qubits can exchange energy via a Jaynes-cummings like interaction. The individual qubits are driven externally to manipulate their states and control their entanglement. We find that the entanglement creates a nontrivial entropy flow which is purely quantum mechanical and can not be associated with the heat flow through the system. By manipulating the entanglement we can manipulate this new flow to either increase or reduce the total entropy flow.