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We consider the steady-state behavior of pairs of active particles havingdifferent persistence times and diffusivities. To this purpose we employ theactive Ornstein-Uhlenbeck model, where the particles are driven by colorednoises with exponential correlation functions whose intensities and correlationtimes vary from species to species. By extending Fox's theory to manycomponents, we derive by functional calculus an approximate Fokker-Planckequation for the configurational distribution function of the system. Afterillustrating the predicted distribution in the solvable case of two particlesinteracting via a harmonic potential, we consider systems of particlesrepelling through inverse power laws potentials. We compare the analyticpredictions to computer simulations for such soft-repulsive interactions in onedimension, and show that at linear order in the persistence times the theory issatisfactory. This work provides the toolbox to qualitatively describemany-body phenomena, such as demixing and depletion, by means of effective pairpotentials.

Effective equilibrium states in mixtures of active particles driven by colored noise