We study a quantum absorption refrigerator, in which a target qubit is cooled by two machine qubits in a nonequilibrium steady-state. It is realized by a strong internal coupling in the two-qubit fridge and a vanishing tripartite interaction among the whole system. The coherence of a machine virtual qubit is investigated as quantumness of the fridge. A necessary condition for cooling shows that the quantum coherence is beneficial to the nonequilibrium fridge, while it is detrimental as far as the maximum coefficient of performance (COP) and the COP at maximum power are concerned. Here, the COP is defined only in terms of heat currents caused by the tripartite interaction, with the one maintaining the two-qubit nonequilibrium state being excluded. The later can be considered to have no direct involvement in extracting heat from the target, as it is not affected by the tripartite interaction.

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We study an endoreversible quantum heat engine in which the heat transfer between the baths is mediated by two qubits. Each qubit acts as an energy filter which allows for the conversion of heat into work. The relation between the efficiency and the power output is derived. It is found that the efficiency of the quantum heat engine at the maximum power output is closely dependent on the properties of quantum dots and does not equal the Curzon-Alhborn efficiency, which is only a function of the bath temperatures. The efficiency and the power output may be adjusted through qubit energy levels. It is further shown that in the limiting cases of small energy levels (or high temperatures) and small temperature differences, the quantum heat engine converges to the classical endoreversible Carnot heat engine.

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