Work and Fluctuations: Coherent vs. Incoherent Ergotropy Extraction

TL;DR

This paper investigates the quantum work extraction process, revealing how coherence affects work fluctuations and introducing a framework that distinguishes between coherent and incoherent ergotropy with analytical solutions for a qubit.

Contribution

It introduces a quasi-probability distribution framework for quantum work, analyzing the trade-off between energy and fluctuations, and highlights the distinct behaviors of coherent versus incoherent ergotropy extraction.

Findings

Positive coherent ergotropy extraction can reduce work fluctuations.

Unlocking ergotropy from coherences leads to diverging fluctuations.

The framework reduces to the TPM scheme for incoherent states.

Abstract

We consider a quasi-probability distribution of work for an isolated quantum system coupled to the energy-storage device given by the ideal weight. Specifically, we analyze a trade-off between changes in average energy and changes in weight's variance, where work is extracted from the coherent and incoherent ergotropy of the system. Primarily, we reveal that the extraction of positive coherent ergotropy can be accompanied by the reduction of work fluctuations (quantified by a variance loss) by utilizing the non-classical states of a work reservoir. On the other hand, we derive a fluctuation-decoherence relation for a quantum weight, defining a lower bound of its energy dispersion via a dumping function of the coherent contribution to the system's ergotropy. Specifically, it reveals that unlocking ergotropy from coherences results in high fluctuations, which diverge when the total coherent energy is unlocked. The proposed autonomous protocol of work extraction shows a significant difference between extracting coherent and incoherent ergotropy: The former can decrease the variance, but its absolute value diverges if more and more energy is extracted, whereas for the latter, the gain is always non-negative, but a total (incoherent) ergotropy can be extracted with finite work fluctuations. Furthermore, we present the framework in terms of the introduced quasi-probability distribution, which has a physical interpretation of its cumulants, is free from the invasive nature of measurements, and reduces to the two-point measurement scheme (TPM) for incoherent states. Finally, we analytically solve the work-variance trade-off for a qubit, explicitly revealing all the above quantum and classical regimes.