  Half of the energy is always lost when charging a capacitor. Even in the
limit of vanishing resistance, half of the charging energy is still lost--to
radiation instead of heat. While this fraction can technically be reduced by
charging adiabatically, it otherwise places a fundamental limit on the charging
efficiency of a capacitor. Here we show that this 1/2 limit can be broken by
coupling a ferroelectric to the capacitor dielectric. Maxwell's equations are
solved for the coupled system to analyze energy flow from the perspective of
Poynting's theorem and show that (1) total energy dissipation is reduced below
the fundamental limit during charging and discharging; (2) energy is saved by
"recycling" the energy already stored in the ferroelectric phase transition;
and (3) this phase transition energy is directly transferred between the
ferroelectric and dielectric during charging and discharging. These results
demystify recent works on low energy negative capacitance devices as well as
lay the foundation for improving fundamental energy efficiency in all devices
that rely on energy storage in electric fields.
