  Despite their fundamentally non-equilibrium nature, the individual and
collective behavior of active systems with polar propulsion and isotropic
interactions (polar-isotropic active systems) are remarkably well captured by
equilibrium mapping techniques. Here we examine two signatures of equilibrium
systems -- the existence of a local free energy function and the independence
of the coarse- grained behavior on the details of the microscopic dynamics --
in polar-isotropic active particles confined by hard walls of arbitrary
geometry at the one-particle level. We find that boundaries that possess
concave regions make the density profile strongly dynamics-dependent and give
it a nonlocal dependence on the geometry of the confining box. This in turn
constrains the scope of equilibrium mapping techniques in polar-isotropic
active systems.
