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Anomalous diffusion is frequently described by scaled Brownian motion (SBM),a Gaussian process with a power-law time dependent diffusion coefficient. Itsmean squared displacement is $\langle x^2(t)\rangle\simeq\mathscr{K}(t)t$ with$\mathscr{K}(t)\simeq t^{\alpha-1}$ for $0<\alpha<2$. SBM may provide aseemingly adequate description in the case of unbounded diffusion, for whichits probability density function coincides with that of fractional Brownianmotion. Here we show that free SBM is weakly non-ergodic but does not exhibit asignificant amplitude scatter of the time averaged mean squared displacement.More severely, we demonstrate that under confinement, the dynamics encoded bySBM is fundamentally different from both fractional Brownian motion andcontinuous time random walks. SBM is highly non-stationary and cannot provide aphysical description for particles in a thermalised stationary system. Ourfindings have direct impact on the modelling of single particle trackingexperiments, in particular, under confinement inside cellular compartments orwhen optical tweezers tracking methods are used.

Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion