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.

• Received 30 March 2012

DOI:https://doi.org/10.1103/PhysRevLett.110.020602