We investigate the dynamics of quantum ergotropy in a multipartite system of two-level atoms interacting with a quantized field. The role of multipartite quantum mutual information and quantum relative entropy is analyzed to understand how correlations and the distinguishability between the passive state and the product of local states affect the extractable work. Numerical results for systems containing two to five atoms show that the maximum ergotropy does not increase linearly with the system size, while the intervals of zero ergotropy are gradually modified and suppressed for larger systems. We also study the effect of the average thermal photon number and different initial atomic states. Increasing the thermal photon number mainly reduces the relative-entropy contribution, whereas the initial state strongly influences both the magnitude and persistence of ergotropy. Among the considered states, the partially entangled state provides the largest and more persistent extractable work, while the mixed GHZ state gives the smallest ergotropy. These results highlight the importance of multipartite correlations, thermal effects, and state preparation in controlling quantum work extraction and may be useful for future studies of quantum batteries and quantum power.
We investigate the dynamics of quantum ergotropy in a multipartite system of two-level atoms interacting with a quantized field. The role of multipartite quantum mutual information and quantum relative entropy is analyzed to understand how correlations and the distinguishability between the passive state and the product of local states affect the extractable work. Numerical results for systems containing two to five atoms show that the maximum ergotropy does not increase linearly with the system size, while the intervals of zero ergotropy are gradually modified and suppressed for larger systems. We also study the effect of the average thermal photon number and different initial atomic states. Increasing the thermal photon number mainly reduces the relative-entropy contribution, whereas the initial state strongly influences both the magnitude and persistence of ergotropy. Among the considered states, the partially entangled state provides the largest and more persistent extractable work, while the mixed GHZ state gives the smallest ergotropy. These results highlight the importance of multipartite correlations, thermal effects, and state preparation in controlling quantum work extraction and may be useful for future studies of quantum batteries and quantum power.
Understanding the role of classical and quantum correlations in work extraction is a problem of fundamental importance in thermodynamics. We approach this problem by considering that, in closed quantum systems, the maximum cyclic work extractable is equal to the ergotropy. Thus, we aim to identify and investigate the contributions to the ergotropy coming from different kinds of initial correlations (total, classical, discord, and entanglement correlations). By doing so, we have introduced and studied quantifiers of correlations which are based on ergotropy. In particular, our results suggest that only discord correlations always give a positive contribution to work extraction, whereas total, classical, and entanglement correlations can reduce the work extraction.
We investigate the decomposition of ergotropy into incoherent and coherent contributions for quantum systems subject to typical Markovian noise channels. The incoherent part originates from population inversion in the energy eigenbasis after dephasing, while the coherent part captures the role of quantum coherence in work extraction. For single-qubit systems, we derive explicit conditions for freezing and enhancement of coherent ergotropy and obtain an analytical upper bound, showing that it cannot exceed one half of the state's quantum coherence. We then study two classes of separable two-qubit states under local noise. For Bell-diagonal states, which are locally completely passive and possess no local coherence, we prove that the total extractable work equals the average of geometric quantum and classical correlations. In this case, coherent ergotropy cannot be enhanced, although freezing occurs under specific noise conditions. By contrast, for separable states with local coherence, coherent ergotropy can increase under all considered noise channels, including phase-flip and depolarizing noise. Extending the analysis to multipartite systems, we show that both the magnitude and range of noise-induced enhancement grow with the number of qubits, indicating collective reinforcement. Finally, we demonstrate through an explicit example that entanglement does not prevent this enhancement: coherent ergotropy may increase under noise even for entangled states. Our results reveal that noise can assist energy storage, challenging the conventional view of noise as purely detrimental and suggesting compatibility between noise-assisted enhancement and fast entanglement-based charging mechanisms in quantum batteries.
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.
The maximum unitarily extractable work from a quantum system---ergotropy---is the basic principle behind quantum batteries, a rapidly emerging field. This work studies ergotropy in two quantum chaotic systems, the quantum kicked top and the kicked Ising spin chain, to illustrate the effects of chaotic dynamics. In an ancilla-assisted scenario, chaos enhances ergotropy when the state is known, a consequence of large entanglement production in the chaotic regime. When the state is unknown, we need to at least partially characterize the state using coarse-grained measurements for useful extraction of work. In this case, chaos impedes ergotropy by suppressing information gained from coarse-grained measurements, while entanglement with an ancilla still facilitates ergotropy. In this scenario, we study the interplay between chaos and entanglement and find a sweet spot in the chaos parameter for optimal work. Our results point to the potential of quantum chaos-assisted batteries for better work extraction.
Abstract It is an established fact that quantum coherences have thermodynamic value. The natural question arises, whether other genuine quantum properties such as entanglement can also be exploited to extract thermodynamic work. In the present analysis, we show that the ergotropy can be expressed as a function of the quantum mutual information, which demonstrates the contributions to the extractable work from classical and quantum correlations. More specifically, we analyze bipartite quantum systems with locally thermal states, such that the only contribution to the ergotropy originates in the correlations. Our findings are illustrated for a two-qubit system collectively coupled to a thermal bath.
Maximum quantum work extraction is generally defined in terms of the ergotropy functional, no matter how experimentally complicated is the implementation of the optimal unitary allowing for it, especially in the case of multipartite systems. In this framework, we consider a quantum battery made up of many interacting subsystems and study the maximum extractable work via concurrent local unitary operations on each subsystem. We call the resulting functional parallel ergotropy. Focusing on the bipartite case, we first observe that parallel ergotropy outperforms work extraction via egoistic strategies, in which the first agent A extracts locally on its part the maximum available work and the second agent B, subsequently, extracts what is left on the other part. For the agents, this showcases the need of cooperating for an overall benefit. Second, from the informational point of view, we observe that the parallel capacity of a state can detect entanglement and compare it with the statistical entanglement witness that exploits fluctuations of stochastic work extraction. Additionally, we face the technical problem of computing parallel ergotropy. We derive analytical upper bounds for specific classes of states and Hamiltonians and provide recipes to obtain numerical upper bounds via semidefinite programming in the generic case. Finally, extending the concept of parallel ergotropy, we demonstrate that system's free-time evolution and application of local unitaries allow one to saturate the gap with the ergotropy of the whole system.