Based on two capacitively coupled quantum dots in the Coulomb-blockade regime, a model of three-terminal quantum-dot refrigerators is proposed. With the help of the master equation, the transport properties of steady-state charge current and energy flow between two quantum dots and thermal reservoirs are revealed. It is expounded that such a structure can be used to construct a refrigerator by controlling the voltage bias and temperature ratio. The thermodynamic performance characteristics of the refrigerator are analyzed, including the cooling power, coefficient of performance (COP), maximum cooling power, and maximum COP. Moreover, the optimal regions of main performance parameters are determined. The influence of dissipative tunnel processes on the optimal performance is discussed in detail. Finally, the performance characteristics of the refrigerators operated in two different cases are compared.

A quantum-dot thermal transistor consisting of three Coulomb-coupled quantum dots coupled to respective electronic reservoirs by tunnel contacts is established. The heat flows through the collector and emitter can be controlled by the temperature of the base. It is found that a small change in the base heat flow can induce a large heat flow change in the collector and emitter. The huge amplification factor can be obtained by optimizing the Coulomb interaction between the collector and the emitter or by decreasing the energy-dependent tunneling rate at the base. The proposed quantum-dot thermal transistor may open up potential applications in low-temperature solid-state thermal circuits at the nanoscale. I. INTRODUCTIONControlling heat flow at the nanoscale has attracted significant attention because of its fundamental and potential applications. 1-3 The thermal diode effect and negative differential thermal resistance (NDTR) are two most important features for building the basic components of functional thermal devices, which are the key tools for the implementation of solid-state thermal circuits. 3,4 The first model of a thermal rectifier/diode was proposed by controlling the heat conduction in one dimensional nonlinear lattice. 5 Based on different microscopic mechanisms, a very significant rectifying effect was exhibited and the concept of NDTR was also proposed in the subsequent works. 6,7 In recent years, the thermal diode effect and NDTR have been extensively studied in the different systems including quantum-dot systems, [8][9][10][11] metal-dielectric interfaces, 12 metal or superconductor systems, [13][14][15][16] quantum Hall conductors, 17 a) Electronic mail: jcchen@xmu.edu.cn 2 / 14 and spin quantum systems. 18 One of the particularly interesting tasks is to further build and implement a thermal transistor, which is analogous to an electronic transistor and can control the heat flows at the collector and emitter by small changes in the temperature or the heat flow at the base. Since Li et al. put forward the first theoretical proposal for a thermal transistor, 7,19 several proposals have been given to design other types of thermal transistors, such as superconductor-normal-metal thermal transistors, 20 near-field thermal transistors, 21 far-field thermal transistors, 22-24 and quantum thermal transistors. 25 Moreover, new concepts for thermal devices such as thermal logical gates 26 and thermal memories 27-29 have also been proposed and demonstrated. In recent years, the electron and heat transport properties of Coulomb-coupled quantum-dot system have been investigated in detail in the thermoelectric generators 30,31 and refrigerators. 32 Moreover, recent experiments have shown that many new applications for Coulomb-coupled quantum-dot system including rectification, 33-35 logical stochastic resonance, 36 and thermal gating 37 can be realized by the voltage fluctuation or thermal fluctuation to control and manage the charge current. Ruokola et al. introduced a single-electron thermal diode consisting...

We calculate the efficiency at the unified trade-off optimization criterion (the so-called maximum Ω criterion) representing a compromise between the useful energy and the lost energy of heat engines operating between two reservoirs at different temperatures and chemical potentials, and demonstrate that the linear coefficient 3/4 and quadratic coefficient 1/32 of the efficiency at maximum Ω are universal for heat engines under strong coupling and symmetry conditions. It is further proved that the conclusions obtained here also apply to the ecological optimization criterion.

We theoretically demonstrate that the heat flows can be manipulated by designing a three-terminal quantum-dot system consisting of three Coulomb-coupled quantum dots connected to respective reservoirs. In this structure, the electron transport between the quantum dots is forbidden, but the heat transport is allowed by the Coulomb interaction to transmit heat between the reservoirs with a temperature difference. We show that such a system is capable of performing thermal management operations, such as heat flow swap, thermal switch, and heat path selector. An important thermal rectifier, i.e., a thermal diode, can be implemented separately in two different paths. The asymmetric configuration of a quantum-dot system is a necessary condition for thermal management operations in practical applications. These results should have important implications in providing the design principle for quantum-dot thermal management devices and may open up potential applications for the thermal management of quantum-dot systems at the nanoscale.

A theoretical proposal that Coulomb-coupled quantum dots can be used as quantum probes to determine the temperature of a sample (i.e., an electronic reservoir) is proposed. Through the regulation of the positive or negative voltage bias in the thermometer, we are able to judge whether the temperature of the sample is higher or lower than that of the reference heat reservoir in the measure environment and to determine the precise temperature of the sample by using a particularly simple temperature-voltage bias relationship in the reversible condition. One outstanding characteristic of the thermometer is that when the sample is at low temperatures, a small temperature change will lead to a large voltage bias change. It means that the proposed thermometer has a high sensitivity when low-temperature samples are measured.