Thermodynamics of the mesoscopic thermoelectric heat engine beyond the linear-response regime

TL;DR

This paper derives a comprehensive expression for the heat current in mesoscopic thermoelectric engines beyond linear response, revealing conditions for Carnot efficiency and the role of quantum constraints on thermodynamics.

Contribution

It provides a clear derivation of heat current beyond linear response and clarifies the conditions for maximum efficiency in mesoscopic thermoelectric engines.

Findings

Efficiency reaches Carnot limit at specific transmission probabilities.

Unitarity of transmission guarantees the second law.

Quantum mechanics constrains thermodynamic performance.

Abstract

Mesoscopic thermoelectric heat engine is much anticipated as a device that allows us to utilize with high efficiency wasted heat inaccessible by conventional heat engines. However, the derivation of the heat current in this engine seems to be either not general or described too briefly, even inappropriate in some cases. In this paper, we give a clear-cut derivation of the heat current of the engine with suitable assumptions beyond the linear-response regime. It resolves the confusion in the definition of the heat current in the linear-response regime. After verifying that we can construct the same formalism as that of the cyclic engine, we find the following two interesting results within the Landauer-B\"uttiker formalism: the efficiency of the mesoscopic thermoelectric engine reaches the Carnot efficiency if and only if the transmission probability is finite at a specific energy and zero otherwise; the unitarity of the transmission probability guarantees the second law of thermodynamics, invalidating Benenti et al.'s argument in the linear-response regime that one could obtain a finite power with the Carnot efficiency under a broken time-reversal symmetry. These results demonstrate how quantum mechanics constraints thermodynamics.