Fluctuations are significant in mesoscopic systems and of particular importance in understanding quantum transport. Here, we show that fluctuations can be considered as a resource for the operations of open quantum systems as functional devices. We derive the statistics of the thermal transistor amplification factor and the cooling-by-heating refrigerator efficiency under the Gaussian fluctuation framework. Statistical properties of the stochastic thermal transistor and the cooling-by-heating efficiency are revealed in the linear-response regime. We clarify the unique role of inelastic processes on thermal transport in mesoscopic systems. We further show that elastic and inelastic processes lead to different bounds based on the linear transport coefficients by using a generic theoretical framework for mesoscopic heat transport, which treats electron and bosonic collective excitations in an equal-footing manner. The underlying physics are illustrated concretely using a double-quantum-dot three-terminal system, though the theory applies to more general systems.

• Received 2 July 2020
• Revised 20 August 2020
• Accepted 24 August 2020

DOI:https://doi.org/10.1103/PhysRevB.102.125405