Quantum Battery: Ergotropy Phase Portrait

A quantum battery — an ensemble of two-level cells charged by a driving field — stores energy that is not always fully recoverable. This 2D simulator drives N battery cells with a resonant Rabi field under pure dephasing and plots the ensemble's coherence directly as a phase-portrait spiral in the (x, y) plane, alongside a population gauge for z and live bars for total stored energy versus ergotropy, the maximum work actually extractable by a unitary operation. As dephasing shrinks the spiral toward the origin, a growing gap opens between stored energy and ergotropy — energy that is stored but thermodynamically stranded as "passive" energy. A toggle between individually-driven and Dicke-style collectively-driven charging shows the well-known quantum speed-up in charging power that collective coupling provides.