# Thermodynamic uncertainty relation in quantum thermoelectric junctions

## TL;DR

This paper investigates the conditions under which the thermodynamic uncertainty relation (TUR) is violated in quantum thermoelectric junctions, revealing that quantum noise can lead to TUR violations, but it always holds near maximum efficiency.

## Contribution

It identifies the quantum noise component responsible for TUR violations and characterizes the parameter regimes where violations occur in quantum thermoelectric systems.

## Key findings

- Quantum noise causes TUR violations in quantum thermoelectric junctions.
- TUR violations are observable in the resonant transport regime.
- TUR always holds near the thermodynamic efficiency limit in noninteracting thermoelectric generators.

## Abstract

Recently, a thermodynamic uncertainty relation (TUR) has been formulated for classical Markovian systems demonstrating trade-off between precision (current fluctuation) and cost (dissipation). Systems that violate the TUR are interesting as they overcome another trade-off relation concerning the efficiency of a heat engine, its power, and its stability (power fluctuations). Here, we analyze the root, extent, and impact on performance of TUR violations in quantum thermoelectric junctions at steady state. Considering noninteracting electrons, first we show that only the "classical" component of the current noise, arising from single-electron transfer events follows the TUR. The remaining, "quantum" part of current noise is therefore responsible for the potential violation of TUR in such quantum systems. Next, focusing on the resonant transport regime we determine the parameter range in which the violation of the TUR can be observed---for both voltage-biased junctions and thermoelectric engines. We illustrate our findings with exact numerical simulations of a serial double quantum dot system. Most significantly, we demonstrate that the TUR always holds in noninteracting thermoelectric generators when approaching the thermodynamic efficiency limit.