Local Temperature of Out-of-Equilibrium Quantum Electron Systems

TL;DR

This paper proposes a consistent method to define and measure the local temperature in out-of-equilibrium quantum electron systems, ensuring it aligns with thermodynamic principles despite the systems not being in local equilibrium.

Contribution

It introduces a framework for defining local temperature using an external probe that satisfies thermodynamic consistency in out-of-equilibrium quantum systems.

Findings

Temperature measured by the probe is independent of coupling details.

Probe temperature matches current-noise based temperature.

The approach satisfies the zeroth law and Carnot's theorem.

Abstract

We show how the local temperature of out-of-equilibrium, quantum electron systems can be consistently defined with the help of an external voltage and temperature probe. We determine sufficient conditions under which the temperature measured by the probe (i) is independent of details of the system-probe coupling, (ii) is equal to the temperature obtained from an independent current-noise measurement, (iii) satisfies the transitivity condition expressed by the zeroth law of thermodynamics, and (iv) is consistent with Carnot's theorem. This local temperature therefore characterizes the system in the common sense of equilibrium thermodynamics, but remains well defined even in out-of-equilibrium situations with no local equilibrium.