\label{ChainWBathsJz0p5}(Left) The battery magnetization as a function of time for different system sizes and (Right) the current as the battery-system junction for \(J_{z}=0.5J\). \(Q(\tau_{i})\) are taken form the simulation with system size \(N=60\) with \(\tau_{1}=0.1N/J\) and \(\tau_{2}=0.5N/J\).