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Self-propelled Brownian particles show rich out-of-equilibrium physics, forinstance, the motility-induced phase separation (MIPS). While decades ofstudying the structure of liquids have established a deep understanding ofpassive systems, not much is known about correlations in active suspensions. Inthis work we derive an approximate analytic theory for three-body correlationsand forces in systems of active Brownian disks starting from the many-bodySmoluchowski equation. We use our theory to predict the conditional forces thatact on a tagged particle and their dependence on the propulsion speed ofself-propelled disks. We identify preferred directions of these forces inrelation to the direction of propulsion and the positions of the surroundingparticles. We further relate our theory to the effective swimming speed of theactive disks, which is relevant for the physics of MIPS. To test and validateour theory, we additionally run particle-resolved computer simulations, forwhich we explicitly calculate the three-body forces. In this context, wediscuss the modeling of active Brownian swimmers with nearly hard interactionpotentials. We find very good agreement between our simulations and numericalsolutions of our theory, especially for the nonequilibrium pair-distributionfunction. For our analytical results, we carefully discuss their range ofvalidity in the context of the different levels of approximation we applied.This discussion allows us to study the individual contribution of particles tothree-body forces and to the emerging structure. Thus, our work sheds light onthe collective behavior, provides the basis for further studies of correlationsin active suspensions, sheds new light onto the collective behavior, and makesa step towards an emerging liquid state theory.

Three-body correlations and conditional forces in suspensions of active hard disks