Abstract In this mini-review, we discuss work extraction under restricted control, where only the system is accessible while other degrees of freedom remain uncontrolled. In this setting, local ergotropy is the maximum work extractable by cyclic unitaries on the system, and it can differ strongly from “switch-off” extraction after quenching the system-environment coupling. We review two settings where correlations and many-body effects shape local work. First, in a two-qubit quantum Rabi model, dissipation induces a Berezinskii–Kosterlitz–Thouless quantum phase transition. A gate-based charge-store-extract protocol uses a decoherence-free state to stabilize storage and makes strong system-bath coupling a resource, yielding local ergotropy above switch-off extraction and making its dynamics transition-dependent, also in relative fluctuations. Second, in a disordered XXZ chain where the first two spins form a battery coupled to an interacting spin bath, local ergotropy shows distinct long-time behavior across Anderson, many-body localized, and ergodic regimes, linking extractable work to localization transitions. Overall, the examples reviewed here show that local ergotropic observables quantify quantum-battery performance under local control and probe collective phenomena.
Abstract In this mini-review, we discuss work extraction under restricted control, where only the system is accessible while other degrees of freedom remain uncontrolled. In this setting, local ergotropy is the maximum work extractable by cyclic unitaries on the system, and it can differ strongly from “switch-off” extraction after quenching the system-environment coupling. We review two settings where correlations and many-body effects shape local work. First, in a two-qubit quantum Rabi model, dissipation induces a Berezinskii–Kosterlitz–Thouless quantum phase transition. A gate-based charge-store-extract protocol uses a decoherence-free state to stabilize storage and makes strong system-bath coupling a resource, yielding local ergotropy above switch-off extraction and making its dynamics transition-dependent, also in relative fluctuations. Second, in a disordered XXZ chain where the first two spins form a battery coupled to an interacting spin bath, local ergotropy shows distinct long-time behavior across Anderson, many-body localized, and ergodic regimes, linking extractable work to localization transitions. Overall, the examples reviewed here show that local ergotropic observables quantify quantum-battery performance under local control and probe collective phenomena.
Abstract We investigate a two-qubit open Rabi model, focusing on local ergotropy-the maximum extractable work by acting solely on the two qubits-within a parameter regime where a Berezinskii–Kosterlitz–Thouless dissipative phase transition occurs. First, we aim to define a protocol for charging, storing, and discharging the two-qubit subsystem, interpreted as the working principle of an open quantum battery. Second, we examine the impact of the phase transition on ergotropy and identify potential markers. To achieve these goals, we construct an ad-hoc charging unitary operator, leveraging our knowledge of the ground state near the transition to bring it into a decoherence-free state (DFS) during storage. Using state-of-the-art numerics based on matrix product state representation, we reveal that high couplings to an external bath approximately double the local ergotropy immediately post-charging. Over time we observe oscillatory behaviors in ergotropy and its fluctuations, which undergo significant changes near the transition, signaling its occurrence. Furthermore, we optimize local ergotropy over time using a physically inspired ansatz, enabling work extraction at a generic time (local ergotropy never reaches zero). Our work proposes a tunable, experimentally realizable protocol for work extraction, leveraging DFS and phase transitions. Additionally, it sheds light on the complex interaction between local ergotropy and quantum phase transitions.
We investigate work extraction in open quantum batteries composed of interacting spin chains weakly coupled to engineered environments. Focusing on two- and four-qubit XX models initially prepared in thermal Gibbs states, we analyze how dissipation and dephasing, acting either locally or collectively, can generate and shape ergotropy during both transient and steady-state dynamics. By introducing a continuous interpolation between parallel and collective noise channels, we systematically characterize the impact of environmental structure on work extractability. We show that purely dissipative dynamics can activate finite ergotropy from completely passive thermal states, giving rise to temperature-dependent transient regimes where hotter initial states temporarily outperform colder ones in an ergotropic Mpemba-like fashion. In contrast, collective dissipation leads to steady states whose passivity crucially depends on the initial temperature and system size, a behavior we trace back to the emergence of non-trivial dark subspaces. Finally, we demonstrate that dephasing channels suppress both transient advantages and steady-state work extraction, highlighting the qualitative difference between dissipative and dephasing environments.
Many-body localization is a dynamical phenomenon characteristic of strongly interacting and disordered many-body quantum systems that fail to achieve thermal equilibrium. From a quantum information perspective, one of the most relevant fingerprints of this phenomenon is the logarithmic growth of the entanglement entropy over time. We perform intensive numerical simulations, applied to a paradigmatic model system, showing that the local ergotropy, the maximum extractable work via local unitary operations on a small subsystem in the presence of Hamiltonian coupling, dynamically witnesses the change from ergodic to localized phases. Within the many-body localized phase, both the local ergotropy and its quantum fluctuations slowly vary over time with a characteristic logarithmic law analogous to the behavior of entanglement entropy. This showcases how directly leveraging local control, instead of local observables or entropies analyzed in previous works, provides a thermodynamic marker of localization phenomena based on the locally extractable work.
We investigate a two-qubit quantum battery where coherent charger-battery coupling competes with non-Markovian environmental interactions. By tuning the coupling strengths and detuning, we identify regimes in which environmental memory enhances energy storage and charging power, while strong dissipation suppresses ergotropy by driving the battery into passive states. We show that detuning plays a dual role: reducing dissipation and inducing a phase shift in the memory kernel that controls the interference between coherent energy exchange and environment-induced backflow. As a result, although the stored energy varies smoothly, the extractable work exhibits a discontinuous onset at a critical detuning, signaling a first-order phase transition in ergotropy. The corresponding phase diagram in the coupling-detuning plane reveals a sharp boundary between thermodynamically inactive and work-producing regimes. Our results demonstrate that phase-controlled coherence and non-Markovianity provide a powerful mechanism for optimizing work extraction in open quantum batteries, offering practical strategies for noise-resilient quantum energy storage.
Going beyond isolated system dynamics, we examine how local and spatially correlated reservoirs influence the work extraction in quantum batteries. By employing a one-dimensional spin-1/2 model coupled to baths via dephasing and amplitude-damping noise, we demonstrate that correlations in reservoirs can significantly enhance battery's performance compared to local noise. In the dephasing scenario, we prove that correlated reservoirs produce a finite amount of extractable work, or ergotropy, during the transient regime when a two-cell battery is initialized in a product state while local noise yields vanishing ergotropy at all times, despite nonvanishing stored energy in both cases. Numerical simulations confirm that this advantage persists across larger system sizes and for both entangled and product initial states. We also find that the dynamics of quantum coherence closely mirror those of ergotropy, highlighting coherence as a key resource underlying the enhanced performance of quantum batteries. Further, we observe that the fraction of stored energy extracted from quantum batteries displays a sharper contrast between the correlated and local reservoirs. Moreover, for dephasing noise, this fraction remains independent of system size, whereas in the amplitude damping case, it exhibits a clear system-size dependence within the transient regime, highlighting distinct operational behaviors under different noise models. In addition, we reveal that when the battery dynamics is governed by an effective Hamiltonian with long-range interactions, it yields higher ergotropy compared to short-range interactions, emphasizing the advantages of reservoir engineering for efficient device design.
We investigate how the spatial arrangement of environment channel influences the dynamics of coherence and work extraction in a two-qubit quantum battery with resonant qubits coupled through an XY-exchange interaction. Qubit B is attached to a finite-temperature thermal bath, while RTN noise is applied either to qubit A or to qubit B, depending on whether it is in a separated or co-located configuration, respectively. Two complementary product states are considered to initialise the coherence on different qubits. The dynamics are evaluated using local l1-norm coherence, global ergotropy and the global-local ergotropy gap. The results suggest that a stronger exchange interaction enhances the redistribution of coherence without necessarily improving retention of extractable work. For the parameter investigated, the greater global ergotropy is retained in the case of the co-located configuration, especially when the initially coherent qubit is not directly affected by the RTN. However, the configuration provides the largest global-local ergotropy gap, which varies with the exchange interaction, initial state and thermal coupling. Suppression of the gap at large J is typically observed in the case of stronger thermalisation, although enhancement of intermediate-coupling may occur. These results establish that total extractable work, local coherence and collective work advantage quantify the distinct aspects of quantum battery performances. The initial distribution of coherence and the spatial arrangement thus provide complementary mechanisms for regulating locally and collectively extractable work in interacting open quantum batteries.