Fundamental precision limits in finite-dimensional quantum thermal machines

TL;DR

This paper establishes fundamental, dynamics-independent precision limits for finite-dimensional quantum thermal machines, revealing how system size, energy bandwidth, and quantum coherence influence achievable measurement accuracy.

Contribution

It derives universal bounds on precision for quantum thermal machines based on system dimensions and energy bandwidth, independent of dynamics, and explores the role of quantum coherence.

Findings

Bounds depend on system dimensions and energy bandwidth.

Quantum coherence can enhance measurement precision.

Trade-off exists between energy storage and charging accuracy.

Abstract

Enhancing the precision of a thermodynamic process inevitably necessitates a thermodynamic cost. This notion was recently formulated as the thermodynamic uncertainty relation, which states that the lower bound on the relative variance of thermodynamic currents decreases as entropy production increases. From another viewpoint, the thermodynamic uncertainty relation implies that if entropy production were allowed to become infinitely large, the lower bound on the relative variance could approach zero. However, it is evident that realizing infinitely large entropy production is infeasible in reality. This indicates that physical constraints impose precision limits on the system, independent of its dynamics. In this study, we derive fundamental precision limits, dynamics-independent bounds on the relative variance and the expectations of observables for open quantum thermal machines operating within a finite-dimensional system and environment. These bounds are set by quantities such as dimensions and energy bandwidth, which depend only on the initial configuration and are independent of the dynamics. Using a quantum battery model, the fundamental precision limits show that there is a trade-off between the amount of energy storage and the charging precision. Additionally, we investigate how quantum coherence affects these fundamental limits, demonstrating that the presence of coherence can improve the precision limits. Our findings provide insights into fundamental limits on the precision of quantum thermal machines.