  Despite its widespread significance, the temporal coupled-mode theory (CMT)
lacks a foundational validation based on electromagnetic principles and stands
as a phenomenological theory relying on fitted coupling coefficients. We employ
an ab initio Maxwellian approach using quasinormal-mode theory to derive an
"exact" Maxwell evolution (EME) equation for resonator dynamics. While the
resulting differential equation bears resemblance to the classical one, it
introduces novel terms embodying distinct physics, suggesting that the CMT
predictions could be faulted by dedicated experiments, for instance carried out
with short and off-resonance pulses, or with resonators of sizes comparable to
or greater than the wavelength. Nonetheless, our examination indicates that,
despite its inherent lack of strictness, the CMT enables precise predictions
for numerous experiments due to the flexibility provided by the fitted coupling
coefficients. The new EME equation is anticipated to be applicable to all
electromagnetic resonator geometries, and the theoretical approach we have
taken can be extended to other wave physics.
