The Quantum Refrigerator: The quest for absolute zero

TL;DR

This paper investigates the scaling behavior of a quantum refrigerator's cooling power as the cold bath temperature approaches absolute zero, revealing a $T_c^{3/2}$ dependence that relates to the third law of thermodynamics.

Contribution

It provides analytical solutions and numerical analysis of a quantum refrigerator cycle, establishing the $T_c^{3/2}$ scaling law for optimal cooling power.

Findings

Optimal cooling rate scales as $T_c^{3/2}$

Linear relations characterize the optimal cycle

Comparison of analytical solutions with numerical optimization

Abstract

The scaling of the optimal cooling power of a reciprocating quantum refrigerator is sought as a function of the cold bath temperature as $T_c \to 0$. The working medium consists of noninteracting particles in a harmonic potential. Two closed-form solutions of the refrigeration cycle are analyzed, and compared to a numerical optimization scheme, focusing on cooling toward zero temperature. The optimal cycle is characterized by linear relations between the heat extracted from the cold bath, the energy level spacing of the working medium and the temperature. The scaling of the optimal cooling rate is found to be proportional to $T_c^{3/2}$ giving a dynamical interpretation to the third law of thermodynamics.