Quantum speed limit, furnishing a lower bound on the required time for theevolution of a quantum system through the state space, imposes an ultimatenatural limitation to the dynamics of physical devices. Quantum absorptionrefrigerators, on the other hand, have attracted a great deal of attention inthe last few years. In this article, we discuss the effects of quantum speedlimit on the performance of a quantum absorption refrigerator. In particular,we show that there exists a trade-off relation between the steady cooling rateof the refrigerator and the minimum time taken to reach the steady state. Basedon this, we define a figure of merit called "bounding second order coolingrate" and show that this scales linearly with the unitary interaction strengthamong the constituent qubits. We also study the increase of bounding secondorder cooling rate with the thermalization strength. We subsequentlydemonstrate that coherence in the initial three qubit system can significantlyincrease the bounding second order cooling rate. We study the efficiency of therefrigerator at maximum bounding second order cooling rate and, in a limitingcase, we show that the efficiency at maximum bounding second order cooling rateis given by a simple formula reminiscent of the Curzon-Ahlborn relation.
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