Dynamics of Work Extraction in Multipartite Atomic Systems: Role of Correlations and Relative Entropy

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.