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Temperature and Voltage

  • Abhay Shastry
Chapter
Part of the Springer Theses book series (Springer Theses)

Abstract

Outside equilibrium, the definition of basic thermodynamic observables such as temperature and voltage are muddled by a competing panoply of “operation definitions” which are often contradictory. Here we define temperature and voltage on an equal footing by means of an equilibrium probe reservoir (such as an STM) coupled locally to the nonequilibrium system of interest; The temperature and voltage measurement are defined by requiring vanishing charge and heat dissipation into the probe. We show that temperature and voltage measurements are unique when they exist. We further derive a necessary and sufficient condition for the existence of a positive temperature solution. We then show that, when a positive temperature solution doesn’t exist, there must exist a negative temperature solution. The latter condition corresponds to a net population inversion. Therefore, a solution always exists. Our results suggest that a local temperature measurement without a simultaneous local voltage measurement, or vice-versa, is a misleading characterization of the state of the nonequilibrium system of interest. These results show an intimate connection to statements of the second law of thermodynamics. We see that the uniqueness of the (simultaneous) measurement of temperature and voltage is related to the Onsager’s statement of the second law of thermodynamics. Therefore, as an intermediate step, we provide the first proof for Onsager’s phenomenological statement (1931) for the case of quantum thermoelectric transport.

Keywords

Temperature measurement Voltage measurement Uniqueness of solution Existence of solution Ideal probe Pathological probe Onsager’s statement of the second law Particle current Heat current Current gradients Negative temperature Population inversion Nonequilibrium distribution function 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Abhay Shastry
    • 1
  1. 1.Department of ChemistryUniversity of TorontoTorontoCanada

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