Power functional theory for the dynamic test particle limit

For classical Brownian systems both in and out of equilibrium we extend the power functional formalism of Schmidt and Brader (2013 J. Chem. Phys. 138 214101) to mixtures of different types of particles. We apply the framework to develop an exact dynamical test particle theory for the self and distinct parts of the van Hove function, which characterize tagged and collective particle motion. The memory functions that induce non-Markovian dynamics are related to functional derivatives of the excess (over ideal) free power dissipation functional. The method offers an alternative to the recently found nonequilibrium Ornstein-Zernike relation for dynamic pair correlation functions.