  The photonic Bose$-$Einstein condensate is a recently observed collective
ground state of a coupled light-matter system. We describe this quantum state
based on macroscopic quantum electrodynamics in dispersing and absorbing
environments. To model the coupled photon$-$dye dynamics, we derive a master
equation using a nested open quantum systems approach yielding all parameters
essential to describe the condensation process. This approach allows us to
describe photon condensates of arbitrary shapes because all geometry-dependent
decay constants can be expressed in terms of the Green's tensor. In particular,
we obtain the cavity mode absorption and emission rates of the dye molecules.
