Violation of the zeroth law of thermodynamics for a non-ergodic interaction

TL;DR

This paper demonstrates that non-ergodic quantum systems can violate the zeroth law of thermodynamics, showing that such systems do not necessarily equilibrate to the reservoir temperature, challenging traditional thermodynamic assumptions.

Contribution

It provides a detailed example of a quantum system that violates the zeroth law due to non-ergodic interactions, highlighting a fundamental exception in thermodynamics.

Findings

A detuned 2-level system does not relax to the reservoir temperature.

The system acquires the reservoir's level-occupation-ratio instead.

Violation of the zeroth law can occur in simple quantum systems.

Abstract

The phenomenon described by our title should surprise no one. What may be surprising though is how easy it is to produce a quantum system with this feature; moreover, that system is one that is often used for the purpose of showing how systems equilibrate. The violation can be variously manifested. In our detailed example, bringing a detuned 2-level system into contact with a monochromatic reservoir does not cause it to relax to the reservoir temperature; rather, the system acquires the reservoir's level-occupation-ratio.