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Physical Review A

Experimental extraction and dynamics of ergotropy in open quantum systems

Hong-Xu Gao, Xu-Cai Zhuang, Qing-Feng Xue, Qi Zhang, Ying-Jie Zhang, Yun‐Jie Xia, Zhong‐Xiao Man

Published Apr 28, 2026• 2 citations
Publisher
DOI
10.1103/prsk-v1q2

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Abstract In many standard analyses of quantum thermodynamics, the system and its environment are assumed to be initially independent and free of any correlations. However, in many physical scenarios, initial system-environment correlations are unavoidable. In this work, we investigate the role of initial system-environment correlations in work extraction from open quantum systems. Furthermore, we examine the effects of these correlations and the nature of environmental dynamics on the evolution of coherence, coherence-based ergotropy, and total ergotropy. In both Markovian and non-Markovian regimes, we show that initial correlations directly influence the amount of ergotropy. We also demonstrate that in the non-Markovian regime, reducing the initial correlation enables optimal utilization of memory effects and maintains work extraction efficiency over longer time intervals. In contrast, in the Markovian regime, such correlations only accelerate the decay process without producing a revival of quantum resources; therefore, work extraction must be carried out within very short time intervals.
We show that it is possible to have nonzero ergotropy in the steady states of an open quantum system consisting of qubits that are collectively coupled to a thermal bath at a finite temperature. The dynamics of our model leads the qubits into a steady state that has coherences in the energy eigenbasis when the system consists of more than a single qubit. We observe that even though the system does not have inverted populations, it is possible to extract work from the coherences and we analytically show that in the high-temperature limit, ergotropy per unit energy is equal to the l_{1} norm of coherence for the two-qubit case. Further, we analyze the scaling of coherence and ergotropy as a function of the number of qubits in the system for different initial states. Our results demonstrate that one can design a quantum battery that is charged by a dissipative thermal bath in the weak-coupling regime.
Ergotropy, the maximum work extractable from a quantum system, is a central resource in quantum physics. Computing ergotropy is well established when the system state is fully known, but its estimation under partial information remains an open problem. Here we introduce a general certification framework that lower bounds ergotropy using only the expectation values of a limited set of arbitrary observables. The method naturally applies in the finite-statistics regime, yielding confidence-certified bounds that explicitly incorporate shot noise. We benchmark our approach on both synthetic data and experimental measurements from an IBM quantum processor. This establishes a robust and experimentally accessible tool for certifying extractable work in realistic quantum settings.