Temperature and voltage measurement in quantum systems far from equilibrium

Shastry, Abhay; Stafford, Charles A.

doi:10.1103/physrevb.94.155433

Title: Temperature and voltage measurement in quantum systems far from equilibrium

Journal Article · Wed Oct 19 00:00:00 EDT 2016 · Physical Review B

DOI:https://doi.org/10.1103/physrevb.94.155433· OSTI ID:1535779

Shastry, Abhay ^[1]; Stafford, Charles A. ^[1]

Univ. of Arizona, Tucson, AZ (United States)

In this work, 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.

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Research Organization:: Univ. of Arizona, Tucson, AZ (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: SC0006699

OSTI ID:: 1535779

Alternate ID(s):: OSTI ID: 1329348

Journal Information:: Physical Review B, Vol. 94, Issue 15; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 15 works

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