Quantum heat engines and refrigerators: Continuous devices

Abstract

Quantum thermodynamics supplies a consistent description of quantum heat engines and refrigerators up to the level of a single few level system coupled to the environment. Once the environment is split into three;a hot, cold and work reservoirs a heat engine can operate. The device converts the positive gain into power;where the gain is obtained from population inversion between the components of the device. Reversing the operation transforms the device into a quantum refrigerator. The quantum tricycle, a device connected by three external leads to three heat reservoirs is used as a template for engines and refrigerators. The equation of motion for the heat currents and power can be derived from first principle. Only a global description of the coupling of the device to the reservoirs is consistent with the first and second laws of thermodynamics. Optimisation of the devices leads to a balanced set of parameters where the couplings to the three reservoirs are of the same order and the external driving field is in resonance. When analysing refrigerators special attention is devoted to a dynamical version of the third law of thermodynamics. Bounds on the rate of cooling when approaching the absolute zero are obtained by optimising the cooling current. At low temperature all refrigerators show universal behavior. Restrictions on the system imposed by the dynamical version of the third law are studied.