The thermodynamic meaning of local temperature of nonequilibrium open quantum systems

TL;DR

This paper investigates the physical meaning of local temperature in nonequilibrium quantum systems, clarifying how different definitions relate to thermodynamic concepts through analytical and numerical analysis of quantum dot models.

Contribution

It compares two definitions of local temperature in nonequilibrium quantum systems and establishes the thermodynamic significance of the minimal-perturbation approach.

Findings

The minimal-perturbation local temperature correlates with equilibrium thermodynamics.

Zero-current temperature is not directly measurable or physically meaningful.

The approach applies to both noninteracting and strongly-correlated regimes.

Abstract

Measuring the local temperature of nanoscale systems out of equilibrium has emerged as a new tool to study local heating effects and other local thermal properties of systems driven by external fields. Although various experimental protocols and theoretical definitions have been proposed to determine the local temperature, the thermodynamic meaning of the measured or defined quantities remains unclear. By performing analytical and numerical analysis of bias-driven quantum dot systems both in the noninteracting and strongly-correlated regimes, we elucidate the underlying physical meaning of local temperature as determined by two definitions: the zero-current condition that is widely used but not measurable, and the minimal-perturbation condition that is experimentally realizable. We show that, unlike the zero-current one, the local temperature determined by the minimalperturbation protocol establishes a quantitative correspondence between the nonequilibrium system of interest and a reference equilibrium system, provided the probed system observable and the related electronic excitations are fully local. The quantitative correspondence thus allows the well-established thermodynamic concept to be extended to nonequilibrium situations.