  We show that for a quantum system coupled to both vibrational and
electromagnetic environments, enforcing additivity of their combined influences
results in non-equilibrium dynamics that does not respect the Franck-Condon
principle. We overcome this shortcoming by employing a collective coordinate
representation of the vibrational environment, which permits the derivation of
a non-additive master equation. When applied to a two-level emitter our
treatment predicts decreasing photon emission rates with increasing vibrational
coupling, consistent with Franck-Condon physics. In contrast, the additive
approximation predicts the emission rate to be completely insensitive to
vibrations. We find that non-additivity also plays a key role in the stationary
non-equilibrium model behaviour, enabling two-level population inversion under
incoherent electromagnetic excitation.
