The study of quantum thermal machines, and more generally of open quantum systems, often relies on master equations. Two approaches are mainly followed. On the one hand, there is the widely used, but often criticized, local approach, where machine sub-systems locally couple to thermal baths. On the other hand, in the more established global approach, thermal baths couple to global degrees of freedom of the machine. There has been debate as to which of these two conceptually different approaches should be used in situations out of thermal equilibrium. Here we compare the local and global approaches against an exact solution for a particular class of thermal machines. We consider thermodynamically relevant observables, such as heat currents, as well as the quantum state of the machine. Our results show that the use of a local master equation is generally well justified. In particular, for weak inter-system coupling, the local approach agrees with the exact solution, whereas the global approach fails for non-equilibrium situations. For intermediate coupling, the local and the global approach both agree with the exact solution and for strong coupling, the global approach is preferable. These results are backed by detailed derivations of the regimes of validity for the respective approaches.or more concretely of an electrical current [34,[42][43][44], the refrigeration of a quantum degree of freedom [45][46][47][48][49][50], the creation of entanglement [51][52][53], the determination of low temperatures [54], or the design of thermal transistors [55] and autonomous quantum clocks [56].The standard description of these systems crucially relies on Markovian master equations to predict the relevant observables, such as heat currents and power. Two main approaches are followed in the literature. The first is a local approach, where the thermal baths couple locally to sub-systems of the machine. The second is a global approach, where thermal baths couple to the global eigenmodes of the machine. As the two approaches are conceptually different, there has been considerable debate about which one should be used in order to accurately describe thermal machines, and more generally out-of-equilibrium systems. Since the global approach describes equilibrium situations accurately (see below), while the local in some cases does not, there has been incentive to use the global approach out of equilibrium as well. Furthermore, the local approach is often believed to be more phenomenological in nature [13,14,19,28,57] and it was even argued that it is unphysical in certain regimes [27,58,59].The goal of the present work is to discuss these questions in depth. We will consider a system for which the full unitary dynamics of the machine and the thermal baths can be solved exactly. This allows us to evaluate the performance of local and global master equations for the machine against the exact dynamics. In addition, we give detailed derivations of the local and the global approaches and discuss the involved approximations. Specifically, ...

We propose and analyze a simple mesoscopic quantum heat engine that exhibits both high-power and highefficiency. The system consists of a biased Josephson junction coupled to two microwave cavities, with each cavity coupled to a thermal bath. Resonant Cooper pair tunneling occurs with the exchange of photons between cavities, and a temperature difference between the baths can naturally lead to a current against the voltage, and hence work. As a consequence of the unique properties of Cooper-pair tunneling, the heat current is completely separated from the charge current. This combined with the strong energy-selectivity of the process leads to an extremely high efficiency. PACS numbers: 85.80.Fi, 85.25.Cp, 42.50.Lc Introduction. Quantum heat engines are devices that convert heat into work which are described by the laws of quantum mechanics. In addition to possible energy-harvesting and refrigeration applications, these devices provide a testbed for the study of thermodynamics in quantum systems.1,2 Several proposals for thermoelectric heat engines have been put forward including systems based on quantum dots 3,4 and coherent interferometers.5 Approaches using a heat source which does not exchange particles with the conductor 3,[6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] are attractive, as they more easily allow the establishment of a thermal gradient. Of these, proposals using microwave photons to mediate the heat flux 10,25,26 are particularly promising, as they allow for a macroscopic spatial separation of hot and cold reservoirs, and because of the rapid progress in relevant experiments on hybrid cavity-conductor systems.

We propose the use of a quantum thermal machine for low-temperature thermometry. A hot thermal reservoir coupled to the machine allows for simultaneously cooling the sample while determining its temperature without knowing the model-dependent coupling constants. In its most simple form, the proposed scheme works for all thermal machines that perform at Otto efficiency and can reach Carnot efficiency. We consider a circuit QED implementation that allows for precise thermometry down to ∼15  mK with realistic parameters. Based on the quantum Fisher information, this is close to the optimal achievable performance. This implementation demonstrates that our proposal is particularly promising in systems where thermalization between different components of an experimental setup cannot be guaranteed.

An implementation of a small quantum absorption refrigerator in a circuit QED architecture is proposed. The setup consists of three harmonic oscillators coupled to a Josephson junction. The refrigerator is autonomous in the sense that it does not require any external control for cooling, but only thermal contact between the oscillators and heat baths at different temperatures. In addition, the setup features a built-in switch, which allows the cooling to be turned on and off. If timing control is available, this enables the possibility for coherence-enhanced cooling. Finally, we show that significant cooling can be achieved with experimentally realistic parameters and that our setup should be within reach of current technology.