Purity and bound energy in ancilla-assisted work extraction

We investigate ancilla-assisted work extraction in quantum batteries from the perspective of bound energy and purity. We show that the bound energy of the reduced system provides a tight upper bound to the daemonic gain and that this bound is saturated for globally pure system-ancilla states. Motivated by this relation, we introduce a purity-based gain that qualitatively predicts the daemonic gain without requiring explicit optimization over measurements. We further develop a framework to analyze the roles of dissipation and intrinsic interactions in daemonic work extraction. Under a collective environment, dissipation can dynamically generate and stabilize finite daemonic gain through environment-induced correlations. In interacting systems, level crossings and spectral restructuring strongly modify the attainable gain through their influence on the accessible bound energy. Our results demonstrate that daemonic gain is governed not only by correlations, but also by the spectral structure and dissipative dynamics of the underlying system, with bound energy and purity providing complementary indicators of its thermodynamic utility.