  We consider the steady-state behavior of pairs of active particles having
different persistence times and diffusivities. To this purpose we employ the
active Ornstein-Uhlenbeck model, where the particles are driven by colored
noises with exponential correlation functions whose intensities and correlation
times vary from species to species. By extending Fox's theory to many
components, we derive by functional calculus an approximate Fokker-Planck
equation for the configurational distribution function of the system. After
illustrating the predicted distribution in the solvable case of two particles
interacting via a harmonic potential, we consider systems of particles
repelling through inverse power laws potentials. We compare the analytic
predictions to computer simulations for such soft-repulsive interactions in one
dimension, and show that at linear order in the persistence times the theory is
satisfactory. This work provides the toolbox to qualitatively describe
many-body phenomena, such as demixing and depletion, by means of effective pair
potentials.
