Abstract. When deriving a master equation for a multipartite weakly-interacting open quantum systems, dissipation is often addressed locally on each component, i.e. ignoring the coherent couplings, which are later added 'by hand'. Although simple, the resulting local master equation (LME) is known to be thermodynamically inconsistent. Otherwise, one may always obtain a consistent global master equation (GME) by working on the energy basis of the full interacting Hamiltonian. Here, we consider a two-node 'quantum wire' connected to two heat baths. The stationary solution of the LME and GME are obtained and benchmarked against the exact result. Importantly, in our model, the validity of the GME is constrained by the underlying secular approximation. Whenever this breaks down (for resonant weakly-coupled nodes), we observe that the LME, in spite of being thermodynamically flawed: (a) predicts the correct steady state, (b) yields with the exact asymptotic heat currents, and (c) reliably reflects the correlations between the nodes. In contrast, the GME fails at all three tasks. Nonetheless, as the inter-node coupling grows, the LME breaks down whilst the GME becomes correct. Hence, the global and local approach may be viewed as complementary tools, best suited to different parameter regimes.

The performance enhancements observed in various models of continuous quantum thermal machines have been linked to the buildup of coherences in a preferred basis. But, is this connection always an evidence of 'quantum-thermodynamic supremacy'? By force of example, we show that this is not the case. In particular, we compare a power-driven three-level continuous quantum refrigerator with a four-level combined cycle, partly driven by power and partly by heat. We focus on the weak driving regime and find the four-level model to be superior since it can operate in parameter regimes in which the three-level model cannot, it may exhibit a larger cooling rate, and, simultaneously, a better coefficient of performance. Furthermore, we find that the improvement in the cooling rate matches the increase in the stationary quantum coherences exactly. Crucially, though, we also show that the thermodynamic variables for both models follow from a classical representation based on graph theory. This implies that we can build incoherent stochastic-thermodynamic models with the same steady-state operation or, equivalently, that both coherent refrigerators can be emulated classically. More generally, we prove this for any N-level weakly driven device with a 'cyclic' pattern of transitions. Therefore, even if coherence is present in a specific quantum thermal machine, it is often not essential to replicate the underlying energy conversion process.

The steady state heat currents of continuous absorption machines can be decomposed into thermodynamically consistent contributions, each of them associated with a circuit in the graph representing the master equation of the thermal device. We employ this tool to study the functioning of absorption refrigerators and heat transformers with an increasing number of active levels. Interestingly, such an analysis is independent of the particular physical implementation (classical or quantum) of the device. We provide new insights into the understanding of scaling up thermal devices concerning both the performance and the magnitude of the heat currents. Indeed, it is shown that the performance of a multilevel machine is smaller or equal than the corresponding to the largest circuit contribution. Besides, the magnitude of the heat currents is well-described by a purely topological parameter which in general increases with the connectivity of the graph. Therefore, we conclude that for a fixed number of levels, the best of all different constructions of absorption machines is the one whose associated graph is as connected as possible, with the condition that the performance of all the contributing circuits is equal.The analysis of the thermodynamic quantities can be realized at different levels of description [24]. From a macroscopic point of view, where the relevant quantities are the bath temperatures and the physical (total) heat currents, to a microscopic description that considers in addition the device structure. This latter perspective is more and more relevant as the advance of the experimental techniques allows for the design and the manipulation of the device. A prominent tool for this microscopic analysis is graph theory, where the stochastic master equation for the populations is represented by a graph. Schnakenberg theory [25] is a popular approach that gives a decomposition of the total entropy production based on a set of fundamental circuits in the graph. Basically, Schnakenberg applies Kirchhoff's current laws to reduce the number of terms appearing in the entropy production, which may be highly beneficial for optimization procedures. It has been used for example in linear irreversible thermodynamics [26] and in the study of steady-state fluctuation theorems [27,28]. This method does not intend to associate an entropy production with each circuit. In particular, the attempt to interpret individually each term in the decomposition may lead to apparent negative entropy productions, although this problem can be avoided by a convenient choice of the fundamental circuits [29][30][31]. However, it has been shown that the diagnosis of the machine performance greatly benefits from considering the thermodynamic analysis of not only the fundamental but all the possible circuits in the graph [32][33][34]. A convenient approach is then Hill theory [35]. Schnakenberg and Hill theory assign the same affinity to each circuit, but the latter considers all the possible circuits and leads to thermodynamically consistent ent...

We propose a three-qubit setup for the implementation of a variety of quantum thermal machines where all heat fluxes and work production can be controlled. An important configuration that can be designed is that of an absorption refrigerator, extracting heat from the coldest reservoir without the need of external work supply. Remarkably, we achieve this regime by using only two-body interactions instead of the widely employed threebody interactions. This configuration could be more easily realised in current experimental setups. We model the open-system dynamics with both a global and a local master equation thermodynamic-consistent approach. Finally, we show how this model can be employed as a heat valve or thermal transistor, in which by varying the local field of one of the two qubits allows one to control and amplify the heat current between the other qubits.