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Characterization of diffusion processes by the distribution of diffusivities

Many transport phenomena in physical and biological systems are described by diffusion processes. The observation of individual particles such as tracer molecules offers an interesting approach to characterize the motion by single-particle tracking (SPT). The observed trajectories are typically analyzed by mean-squared displacements. However, this method conceals significant properties of the motion in inhomogeneous systems due to averaging along a trajectory or over an ensemble. Hence, instead of averaging we introduced an analysis which considers diffusivities D defined as scaled squared displacements during a time lag τ along a trajectory in the distribution of diffusivities p(D,τ) [1]. This distribution describes the diffusivity as a fluctuating quantity and allows further analysis of statistical properties. It should be noted that the first moment of the distribution corresponds to the slope of the well-known mean-squared displacements and identifies the mean diffusion coefficient of the system.