The breakdown of the zeroth law of thermodynamics and the definition of temperature in small quantum systems

TL;DR

This paper demonstrates that the zeroth law of thermodynamics breaks down in small quantum systems at low temperatures, challenging traditional temperature definitions and proposing an alternative method using an auxiliary thermometer site.

Contribution

It reveals the failure of the zeroth law in small quantum systems and introduces a new temperature definition using an auxiliary site as a thermometer.

Findings

Small quantum systems are not in thermal equilibrium with each other at low temperatures.

Traditional temperature definitions fail due to the breakdown of transitive thermal equilibrium.

A new temperature measurement method using an auxiliary site is proposed.

Abstract

We study two small quantum systems coupled to the same reservoir which is in thermal equilibrium. By studying the particle density and the energy density in the two systems before and after they contact each other, we find that the two systems are not in thermal equilibrium with each other. Our result shows that the zeroth law of thermodynamics is broken in small quantum systems at low temperatures. Therefore, the traditional way of defining temperature fails due to the breakdown of the transitive relation of thermal equilibrium. Then we show a different way of defining temperature by attaching an auxiliary site, which plays the role of a thermometer, to the small quantum system.