Gaussianity Fair: The Riddle of Anomalous yet Non-Gaussian Diffusion.

Single particle tracking has become a standard method, especially in biophysics (1,2). With superresolution microscopy, the motions of even individual molecules in a live cell are routinely tracked (1–3). The monitored dynamics provides important clues on the interactions of the probe particle with the intracellular environment. The results from such studies are quite remarkable. First, they demonstrate the existence of anomalous particle diffusion of the form hr2ixta with as1 at often macroscopic times (1,2). Second, the observed motion may turn out to be pronouncedly nonstationary: this causes the time-averaged mean squared displacement d, typically evaluated from measured time series of the particle trajectories, to behave fundamentally differently from the ensemble analog hr2i (4,5). In addition to this, subdiffusive particle motion may exhibit aging, that is, its dynamics changes over time: typically, the particle slows down in the sense that in d the effective diffusivity decays with the trace length t (5,6). However, in the strongly nonequilibrium setting of biological cells, reinforcing aging may also emerge, when the power of the t dependence is positive. The inequivalence d2shr2i and aging is not