  The equations of motion of active systems can be modeled in terms of
Ornstein-Uhlenbeck processes (OUPs) with appropriate correlators. For further
theoretical studies, these should be approximated to yield a Markovian picture
for the dynamics and a simplified steady-state condition. We perform a
comparative study of the Unified Colored Noise Approximation (UCNA) and the
approximation scheme by Fox recently employed within this context. We review
the approximations necessary to define effective interaction potentials in the
low-density limit and study the conditions for which these represent the
behavior observed in two-body simulations for the OUPs model and Active
Brownian particles. The demonstrated limitations of the theory for potentials
with a negative slope or curvature can be qualitatively corrected by a new
empirical modification. In general, we find that in the presence of
translational white noise the Fox approach is more accurate. Finally, we
examine an alternative way to define a force-balance condition in the limit of
small activity.
