  Active particles driven by colored noise can be approximately mapped onto a
system that obeys detailed balance. The effective interactions which can be
derived for such a system allow to describe the structure and phase behavior of
the active fluid by means of an effective free energy. In this paper we explain
why the related thermodynamic results for pressure and interfacial tension do
not represent the results one would measure mechanically. We derive a dynamical
density functional theory, which in the steady state simultaneously validates
the use of effective interactions and provides access to mechanical quantities.
Our calculations suggest that in the colored-noise model the mechanical
pressure in coexisting phases might be unequal and the interfacial tension can
become negative.
