  The quark meson (linear sigma) model with linearized fluctuations displays at
a critical end point the onset of a curve of first-order phase transitions
(FOPTs) located at non-zero chemical potentials and temperatures below a
certain cross-over temperature. The model qualifies well for an illustrative
example to study the impact of the emerging FOPT, e.g. on photon emissivities.
Such a case study unravels the tight interlocking of the phase structure with
the emission rates, here calculated according to lowest-order tree level
processes by kinetic theory expressions. It is the strong dependence of the
rates on the effective masses of the involved degrees of freedom which
distinctively vary over the phase diagram thus shaping the emissivity
accordingly. At the same time, thermodynamic properties of the medium are
linked decisively to these effective masses, i.e. a consistent evaluation of
thermodynamics, governing for instance adiabatic expansion paths, and emission
rates is maintained within such an approach.
