Quantum refrigerators and the third law of thermodynamics

TLDR

The refrigerator is a nonlinear device that merges currents from a cold bath, a hot entropy sink, and a driving bath providing cooling power. The study investigates how the cooling rate of a quantum bath behaves as its temperature approaches absolute zero. The authors quantify the third law by evaluating the cooling exponent ζ in a continuous quantum refrigerator model using coupled oscillators or two‑level systems, comparing heat‑driven and power‑driven designs, and exploring generic heat‑bath models and periodically driven open‑system theory. Optimized heat‑driven and power‑driven refrigerators yield the same exponent ζ, independent of the working medium or driver, indicating that ζ is set by the cold reservoir’s properties and its interaction, with III‑law constraints on the interaction Hamiltonian discussed.

Abstract

The rate of temperature decrease of a cooled quantum bath is studied as its temperature is reduced to the absolute zero. The III-law of thermodynamics is then quantified dynamically by evaluating the characteristic exponent {\zeta} of the cooling process dT(t)/dt \sim -T^{\zeta} when approaching the absolute zero, T \rightarrow 0. A continuous model of a quantum refrigerator is employed consisting of a working medium composed either by two coupled harmonic oscillators or two coupled 2-level systems. The refrigerator is a nonlinear device merging three currents from three heat baths: a cold bath to be cooled, a hot bath as an entropy sink, and a driving bath which is the source of cooling power. A heat driven refrigerator (absorption refrigerator) is compared to a power driven refrigerator. When optimized both cases lead to the same exponent {\zeta}, showing a lack of dependence on the form of the working medium and the characteristics of the drivers. The characteristic exponent is therefore determined by the properties of the cold reservoir and its interaction with the system. Two generic heat baths models are considered, a bath composed of harmonic oscillators and a bath composed from ideal Bose/Fermi gas. The restrictions on the interaction Hamiltonian imposed by the III-law are discussed. In the appendix the theory of periodicaly driven open systems and its implication to thermodynamics is outlined.