  Active systems, which are driven out of equilibrium by local non-conservative
forces, exhibit unique behaviors and structures with potential utility for the
design of novel materials. An important and difficult challenge along the path
towards this goal is to precisely predict how the structure of active systems
is modified as their driving forces push them out of equilibrium. Here, we use
tools from liquid-state theories to approach this challenge for a classic
minimal active matter model. First, we construct a nonequilibrium mean-field
framework which can predict the structure of systems of weakly interacting
particles. Second, motivated by equilibrium solvation theories, we modify this
theory to extend it with surprisingly high accuracy to systems of strongly
interacting particles, distinguishing it from most existing similarly tractable
approaches. Our results provide insight into spatial organization in strongly
interacting out-of-equilibrium systems.
