Thermodynamic and quantum bounds on nonlinear DC thermoelectric transport

Abstract

I consider the non-equilibrium DC transport of electrons through a quantum system with a thermoelectric response. This system may be any nanostructure or molecule modeled by the nonlinear scattering theory which includes Hartree-like electrostatic interactions exactly, and certain dynamic interaction effects (decoherence and relaxation) phenomenologically. This theory is believed to be a reasonable model when single-electron charging effects are negligible. I derive three fundamental bounds for such quantum systems coupled to multiple macroscopic reservoirs, one of which may be superconducting. These bounds affect nonlinear heating (such as Joule heating), work and entropy production. Two bounds correspond to the first law and second law of thermodynamics in classical physics. The third bound is quantum (wavelength dependent), and is as important as the thermodynamic ones in limiting the capabilities of mesoscopic heat-engines and refrigerators. The quantum bound also leads to Nernst's unattainability principle that the quantum system cannot cool a reservoir to absolute zero in a finite time, although it can get exponentially close.

8pages (2figs) version2 (PRB version) minor improvements of earlier version

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• Cross thermoelectric coupling in normal-superconductor quantum dots
• A hybrid superconducting quantum dot acting as an efficient charge and spin Seebeck diode
• Coherent Long-Range Thermoelectrics in Nonadiabatic Driven Quantum Systems
• Thermoelectric effects in quantum Hall systems beyond linear response
• Spin and charge thermopower of resonant tunneling diodes
• Scattering theory of thermal and bipolar thermoelectric diodes
• Quantum thermocouples: nonlocal conversion and control of heat in nanostructures
• High-performance Andreev interferometer-based electronic coolers
• Illusory cracks in the second law of thermodynamics in quantum nanoelectronics
• Quantum coherent control of linear and nonlinear thermoelectricity on graphene nanostructure heat engines