Temperature and voltage measurement in quantum systems far from equilibrium
Abstract
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.
 Publication:

Physical Review B
 Pub Date:
 October 2016
 DOI:
 10.1103/PhysRevB.94.155433
 arXiv:
 arXiv:1603.00096
 Bibcode:
 2016PhRvB..94o5433S
 Keywords:

 Condensed Matter  Mesoscale and Nanoscale Physics;
 Condensed Matter  Statistical Mechanics;
 Mathematical Physics
 EPrint:
 16 pages, 6 figures