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.

16 pages, 6 figures

References in corpus (13)

• Vibrational and electronic heating in nanoscale junctions
• Heat conduction in molecular transport junctions
• Giant Thermoelectric Effect from Transmission Supernodes
• Quantum Thermodynamics: A Nonequilibrium Green's Functions Approach
• Strong bounds on Onsager coefficients and efficiency for three terminal thermoelectric transport in a magnetic field
• Many-body theory of electronic transport in single-molecule heterojunctions
• Efficiency of three-terminal thermoelectric transport under broken-time reversal symmetry
• Electron transport in a one dimensional conductor with inelastic scattering by self-consistent reservoirs
• Voltage and dephasing probes: a full counting statistics discussion
• Local temperatures of strongly-correlated quantum dots out of equilibrium
• ThermoElectric Transport Properties of a Chain of Quantum Dots with Self-Consistent Reservoirs
• Local Temperatures and Heat Flow in Quantum Driven Systems
• Thermoelectric Corrections to Quantum Voltage Measurement

Cited by in corpus (18)

• Fundamental aspects of steady-state conversion of heat to work at the nanoscale
• Thermometry in the quantum regime: Recent theoretical progress
• Local Temperatures Out of Equilibrium
• Charge Transport and Entropy Production Rate in Magnetically Active Molecular Dimer
• Local entropy of a nonequilibrium fermion system
• Quantum thermodynamics of nanoscale steady states far from equilibrium
• Scanning Tunneling Potentiometry, Charge Transport and Landauer's Resistivity Dipole from the Quantum to the Classical Transport Regime
• The third law of thermodynamics in open quantum systems
• Work Sum Rule for Open Quantum Systems
• Emergence of Fourier's law of heat transport in quantum electron systems
• Effect of quantum resonances on local temperature in nonequilibrium open systems
• Scattering theory of thermal and bipolar thermoelectric diodes
• Scanning Tunneling Thermometry
• Persistent versus dissipative Peltier effect in a topological quantum thermocouple
• Quantum thermocouples: nonlocal conversion and control of heat in nanostructures
• Local heat current flow in ballistic phonon transport of graphene nanoribbons
• Emergence of the 2nd Law in an Exactly Solvable Model of a Quantum Wire
• Thermodynamics of a Quantum Subsystem