Finding the quantum thermoelectric with maximal efficiency and minimal entropy production at given power output

TL;DR

This paper explores the limits of quantum thermoelectric devices, deriving how to maximize power and efficiency at finite power outputs using nonlinear scattering theory, revealing fundamental bounds and the impact of phonon and photon effects.

Contribution

It provides a detailed theoretical framework for optimizing quantum thermoelectrics, including maximum power and efficiency, and addresses the effects of nonlinear phonon and photon interactions.

Findings

Maximum efficiency approaches Carnot limit at zero power

Efficiency decreases with increasing power output

Strong phonon and photon effects can unify maximum efficiency and power

Abstract

We investigate the nonlinear scattering theory for quantum systems with strong Seebeck and Peltier effects, and consider their use as heat-engines and refrigerators with finite power outputs. This article gives detailed derivations of the results summarized in Phys. Rev. Lett. 112, 130601 (2014). It shows how to use the scattering theory to find (i) the quantum thermoelectric with maximum possible power output, and (ii) the quantum thermoelectric with maximum efficiency at given power output. The latter corresponds to a minimal entropy production at that power output. These quantities are of quantum origin since they depend on system size over electronic wavelength, and so have no analogue in classical thermodynamics. The maximal efficiency coincides with Carnot efficiency at zero power output, but decreases with increasing power output. This gives a fundamental lower bound on entropy production, which means that reversibility (in the thermodynamic sense) is impossible for finite power output. The suppression of efficiency by (nonlinear) phonon and photon effects is addressed in detail; when these effects are strong, maximum efficiency coincides with maximum power. Finally, we show in particular limits (typically without magnetic fields) that relaxation within the quantum system does not allow the system to exceed the bounds derived for relaxation-free systems, however, a general proof of this remains elusive.