Performance at maximum figure of merit for a single quantum dot refrigerator

In this paper, we examine the optimal performance characteristics for a single-level quantum dot refrigerator within the framework of ballistic electron transport between two reservoirs. Analytical expressions for the maximum figure of merit were derived. The coefficient of performance at the maximum figure of merit, which depends on the Carnot bound, was analyzed for a refrigerator of the quantum dot system and successfully compared with the maximum cooling power coefficient of performance and the Curzon–Ahlborn coefficient of performance. Besides, the coefficient of performance at the maximum figure of merit of the model was demonstrated through numerical analysis. Our results indicate that the coefficient of performance at maximum cooling power and at maximum figure of merit differs from the maximum cooling power coefficient of performance and the Curzon–Ahlborn coefficient of performance in the limit of a small Carnot coefficient of performance. Optimizing the figure of merit results in the highest coefficient of performance, while optimizing for cooling power leads to the lowest values. It is constrained by an upper bound of Carnot coefficient of performance and a lower bound on the coefficient of performance at maximum cooling power and on the Curzon–Ahlborn coefficient of performance.