Geometric thermodynamic uncertainty relation in periodically driven thermoelectric heat engine

TL;DR

This paper introduces a geometric thermodynamic uncertainty relation for periodically driven thermoelectric heat engines, revealing how geometric effects can enhance efficiency and performance beyond steady-state limits.

Contribution

It uncovers a Berry-phase-like geometric contribution to the thermodynamic uncertainty relation in periodically driven systems, extending the understanding beyond steady-state thermodynamics.

Findings

Periodic driving can outperform steady-state thermoelectric engines.

Derived bounds relate efficiency, power, and constancy in driven systems.

Analytical example with a quantum dot heat engine illustrates the theory.

Abstract

Thermodynamic uncertainty relation, quantifying a trade-off among average current, the associated fluctuation (precision), and entropy production (cost), has been formulated in nonequilibrium steady state and various stochastic systems. Herein, we study the thermodynamic uncertainty relation in generic thermoelectric heat engines under a periodic control protocol, by uncovering the underlying Berry-phase-like contribution. We show that our thermodynamic uncertainty relation breaks the seminal steady-state results, originating from the non-vanishing geometric effect. Furthermore, by deriving the consequent trade-off relation binding efficiency, power, and constancy, we prove that the periodically driven thermoelectric heat engines can generally outperform the steady-state analogies. The general bounds are illustrated by an analytically solvable two-terminal single quantum dot heat engine under the periodic modulation. Our work provides a geometric framework in bounding and optimizing a wide range of periodically driven thermoelectric thermal machines.