Local temperature of an interacting quantum system far from equilibrium

TL;DR

This paper develops a theory for measuring local temperature in interacting quantum systems far from equilibrium using a thermoelectric probe, ensuring consistency with thermodynamic laws under specific conditions.

Contribution

It introduces a comprehensive framework for local temperature measurement in quantum systems, accounting for probe characteristics and thermodynamic law consistency.

Findings

Local temperature measurement aligns with thermodynamic laws under certain conditions.

Non-broad-band probes introduce higher-order corrections to thermodynamic laws.

The theory applies to systems at negative absolute temperature.

Abstract

A theory of local temperature measurement of an interacting quantum electron system far from equilibrium via a floating thermoelectric probe is developed. It is shown that the local temperature so defined is consistent with the zeroth, first, second, and third laws of thermodynamics, provided the probe-system coupling is weak and broad band. For non-broad-band probes, the local temperature obeys the Clausius form of the second law and the third law exactly, but there are corrections to the zeroth and first laws that are higher-order in the Sommerfeld expansion. The corrections to the zeroth and first laws are related, and can be interpreted in terms of the error of a nonideal temperature measurement. These results also hold for systems at negative absolute temperature.