We use the fundamental nonequilibrium steady state fluctuation symmetry and derive a condition on the validity of the thermodynamic uncertainty relation (TUR) in thermal transport problems, classical or quantum alike. We test this condition and study the breakdown of the TUR in different thermal transport junctions of bosonic and electronic degrees of freedom. First, we prove that the TUR is valid in harmonic oscillator junctions. In contrast, in the nonequilibrium spin-boson model, which realizes many-body effects, it is satisfied in the Markovian limit, but violations arise as we tune (reduce) the cutoff frequency of the thermal baths, thus observing non-Markovian dynamics. Finally, we consider heat transport by noninteracting electrons in a tight-binding chain model. Here we show that the TUR is feasibly violated by tuning e.g. the hybridization energy of the chain to the metal leads. These results manifest that the validity of the TUR relies on the statistics of the participating carriers, their interaction, and the nature of their couplings to the macroscopic contacts (metal electrodes, phonon baths).

We formulate a full-counting statistics description to study energy exchange in multi-terminal junctions. Our approach applies to quantum systems that are coupled either additively or nonadditively (cooperatively) to multiple reservoirs. We derive a Markovian Redfield-type equation for the counting-field dependent reduced density operator. Under the secular approximation, we confirm that the cumulant generating function satisfies the heat exchange fluctuation theorem. Our treatment thus respects the second law of thermodynamics. We exemplify our formalism on a multi-terminal two-level quantum system, and apply it to realize the smallest quantum absorption refrigerator, operating through engineered reservoirs, and achievable only through a cooperative bath interaction model. of the current and subsequent suppression with increasing interaction strength, appears once the system-bath interaction energy becomes comparable to the system's natural frequencies.Physically, strong system-bath interactions are responsible for three-phonon (and more) scattering contributions to thermal transport problems, beyond the weak-coupling resonant term. Alternatively, rather than focusing on the distinction between strong and weak-coupling, one may classify system-bath interaction operators based on whether they are additive or non-additive in the different reservoirs. These two classes of models, additive and non-additive, realize distinctive energy transport characteristics and refrigeration as we show in this work.An autonomous absorption refrigerator transfers thermal energy from a cold bath to a hot bath without an input power by using thermal energy provided from a so-called work reservoir. In a recent study [41], we demonstrated that the smallest system, a qubit, is incapable of operating as a quantum absorption refrigerator (QAR) when the baths are coupled weakly-additively to the system. However, we demonstrated that by coupling the system in a non-additive manner to three heat baths, which are spectrally structured, a cooling function was achieved. Moreover, we showed that the system reached the Carnot bound when the reservoirs were characterized by a single frequency component. This study thus clearly illustrates that non-additive models can bring in a new function, which is missing in additive scenarios. On the other hand, as was pointed out in [41] and illustrated earlier on in [35,36,38], the dynamics of non-additive models can be treated with standard kinetic quantum master equations (QMEs), albeit with a non-additive, baths-cooperative dissipator.The objective of this paper is to present a rigorous, thermodynamically consistent formalism for the calculation of energy exchange (current and cumulants) in additive and non-additive interaction models, thus develop the groundwork of the qubit-QAR presented in [41]. Our formalism utilizes a full-counting statistics (FCS) approach that provides cumulants of energy exchange to all orders [26,[42][43][44][45]. In this method, rather than focusing directly on the averaged heat...

Ru nanoparticles deposited onto cellulose nanocrystals are highly active arene hydrogenation catalysts under mild conditions.

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