Thermal Contact: Mischief and Time Scales

TL;DR

This paper explores the quantum conditions necessary for thermalization, emphasizing the importance of local Hamiltonian information in temperature measurement and challenging the notion that rapid interactions naturally lead to thermal equilibrium.

Contribution

It establishes necessary conditions for quantum thermal contact and demonstrates that quick interactions with a reservoir do not guarantee thermalization.

Findings

Temperature measurement requires local Hamiltonian information.

Full state tomography can be fooled into arbitrary temperature readings.

Rapid interactions alone do not ensure thermalization.

Abstract

We discuss what kind of quantum channels can enable thermalization processes. We show that in order to determine a system's temperature, a thermometer needs to dynamically gain information about the system's local Hamiltonian and not just its state. We illustrate this showing that any temperature measurement protocol that does not resolve the system's local Hamiltonian (such as, e.g., full state tomography) is susceptible to being fooled into measuring any value for the temperature. We will establish necessary conditions for thermal contact for quantum systems. Furthermore, we will show that the intuitive idea of thermalization emerging out of quickly interacting with the microconstitutents of a thermal reservoir cannot be correct.