# Power, Efficiency and Fluctuations in a Quantum Point Contact as Steady-State Thermoelectric Heat Engine

## TL;DR

This paper investigates the trade-offs between power, efficiency, and fluctuations in a quantum point contact thermoelectric heat engine, revealing near-maximum power and efficiency with small fluctuations, and extending thermodynamic uncertainty relations.

## Contribution

It provides a detailed theoretical analysis of a QPC as a steady-state heat engine, including power, efficiency, fluctuations, and TUR bounds in both linear and non-linear regimes.

## Key findings

- Power reaches near maximum with over 50% Carnot efficiency.
- Small fluctuations accompany high power and efficiency.
- A stronger TUR bound is derived in the linear regime, applicable beyond linear response.

## Abstract

The trade-off between large power output, high efficiency and small fluctuations in the operation of heat engines has recently received interest in the context of thermodynamic uncertainty relations (TURs). Here we provide a concrete illustration of this trade-off by theoretically investigating the operation of a quantum point contact (QPC) with an energy-dependent transmission function as a steady-state thermoelectric heat engine. As a starting point, we review and extend previous analysis of the power production and efficiency. Thereafter the power fluctuations and the bound jointly imposed on the power, efficiency and fluctuations by the TURs are analyzed as additional performance quantifiers. We allow for arbitrary smoothness of the transmission probability of the QPC, which exhibits a close to step-like dependence in energy, and consider both the linear and the non-linear regime of operation. It is found that for a broad range of parameters, the power production reaches nearly its theoretical maximum value, with efficiencies more than half of the Carnot efficiency and at the same time with rather small fluctuations. Moreover, we show that by demanding a non-zero power production, in the linear regime a stronger TUR can be formulated in terms of the thermoelectric figure of merit. Interestingly, this bound holds also in a wide parameter regime beyond linear response for our QPC device.