  We show that a local measurement of temperature and voltage for a quantum
system in steady state, arbitrarily far from equilibrium, with arbitrary
interactions within the system, is unique when it exists. This is interpreted
as a consequence of the second law of thermodynamics. We further derive a
necessary and sufficient condition for the existence of a solution. In this
regard, we find that a positive temperature solution exists whenever there is
no net population inversion. However, when there is a net population inversion,
we may characterize the system with a unique negative temperature. Voltage and
temperature measurements are treated on an equal footing: They are
simultaneously measured in a noninvasive manner, via a weakly-coupled
thermoelectric probe, defined by requiring vanishing charge and heat
dissipation into the probe. Our results strongly suggest that a local
temperature measurement without a simultaneous local voltage measurement, or
vice-versa, is a misleading characterization of the state of a nonequilibrium
quantum electron system. These results provide a firm mathematical foundation
for voltage and temperature measurements far from equilibrium.
