Optimization of energy production in two-qubit heat engines using the ecological function

Abstract

We study the ecological regime of quantum heat engines where the heat transfer between the environment and the engine is mediated with two qubits that act as energy filters and allow the conversion of heat into work. Using quantum thermodynamics, the theory of open quantum system and the fundamentals of finite-time thermodynamics we obtain the output power, the ecological function and the entropy production of the engine. Then, we optimize the functioning to the ecological function to find the range of efficiencies for which the system works optimally under the ecological criterium. We find that (i) the maximum value of the ecological function depends on the thermal copulings and the energies of the qubits that define the engine. (ii) We can define an ecological working region where the engine works producing a power that is similar to the maximum power but where it rejects much less heat to the environment. (iii) That the range of efficiencies defining the ecological region depends on the parameters defining the engine.(iv) An optimal working region where both the power and the ecological function are big is defined for each machine.