  We investigate the response of a photonic gas interacting with a reservoir of
pumped dye-molecules to quenches in the pump power. In addition to the expected
dramatic critical slowing down of the equilibration time around phase
transitions we find extremely slow equilibration even far away from phase
transitions. This non-critical slowing down can be accounted for quantitatively
by fierce competition among cavity modes for access to the molecular
environment, and we provide a quantitative explanation for this non-critical
slowing down.
