Thermodynamic limits of dynamic cooling

TL;DR

This paper investigates the fundamental limits of dynamic cooling in quantum systems, establishing a positive minimal temperature, analyzing work costs, and exploring different reservoir configurations to understand the unattainability of absolute zero.

Contribution

It explicitly determines the minimal achievable temperature in quantum cooling and analyzes the work cost, providing insights into the third law of thermodynamics in quantum regimes.

Findings

Minimal temperature T_min > 0 is reachable, but absolute zero is unattainable.

Work cost to reach T_min diverges as 1/T_min.

Cooling with large spin reservoirs allows T_min to scale as 1/N.

Abstract

We study dynamic cooling, where an externally driven two-level system is cooled via reservoir, a quantum system with initial canonical equilibrium state. We obtain explicitly the minimal possible temperature $T_{\rm min}>0$ reachable for the two-level system. The minimization goes over all unitary dynamic processes operating on the system and reservoir, and over the reservoir energy spectrum. The minimal work needed to reach $T_{\rm min}$ grows as $1/T_{\rm min}$. This work cost can be significantly reduced, though, if one is satisfied by temperatures slightly above $T_{\rm min}$. Our results on $T_{\rm min}>0$ prove unattainability of the absolute zero temperature without ambiguities that surround its derivation from the entropic version of the third law. The unattainability can be recovered, albeit via a different mechanism, for cooling by a reservoir with an initially microcanonic state. We also study cooling via a reservoir consisting of $N\gg 1$ identical spins. Here we show that $T_{\rm min}\propto\frac{1}{N}$ and find the maximal cooling compatible with the minimal work determined by the free energy.