Aging effects and population splitting in single-particle trajectory averages

We study time averages of single particle trajectories in scale-free anomalous diffusion processes, in which the measurement starts at some time t_a>0 after initiation of the process at t=0. Using aging renewal theory, we show that for such nonstationary processes a large class of observables are affected by a unique aging function, which is independent of boundary conditions or the external forces. Moreover, we discuss the implications of aging induced population splitting: with growing age t _a of the process, an increasing fraction of particles remains motionless in a measurement of fixed duration. Consequences for single biomolecule tracking in live cells are discussed.