Thermodynamic Limits to Anomalous Diffusion

D iffusion is a commonplace phenomenon: Put a droplet of ink into a tank of water, and it will simultaneously spread out and becomemore andmore diluted (Fig. 1). This means that the probability of finding a given ink particle at some position evolves from a sharply peaked distribution to a very broad one (Fig. 2, left). Typically, the width of this distribution, quantified by the variance, increases linearly with time, in line with an empirical law known as Fick’s second law of diffusion. But this law can be defied by systems ranging from themicroscopic (such as biological cells) to the macroscopic (such as astrophysical plasmas), which exhibit anomalous diffusion processes where the variance increases nonlinearly with time [1]. New research by David Hartich and Aljaž Godec, at the Max Planck Institute for Biophysical Chemistry in Germany,