Measurable Consequences of the Local Breakdown of the Concept of Temperature

TL;DR

This paper investigates the breakdown of the concept of temperature at small scales in quantum many-body systems, proposing experimental ways to observe when local temperature definitions fail.

Contribution

It provides examples and experimental proposals to detect the local breakdown of temperature in quantum systems, highlighting the limits of thermodynamic descriptions at small scales.

Findings

Magnetic properties of spin chains are strictly local.

Measurement outcomes indicate whether local states are thermal.

The concept of temperature may not be consistent at small length scales.

Abstract

Local temperature defined by a local canonical state of the respective subsystem, does not always exist in quantum many body systems. Here, we give some examples of how this breakdown of the temperature concept on small length scales might be observed in experiments: Measurements of magnetic properties of an anti-ferromagnetic spin-1 chain. We show that those magnetic properties are in fact strictly local. As a consequence their measurement reveals whether the local (reduced) state can be thermal. If it is, a temperature may be associated to the measurement results, while this would lead to inconsistencies otherwise.