  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.
