The physical mechanisms of anomalous diffusion

Abstract

This paper presents the general mechanisms leading to anomalous diffusion laws. The central point of this analysis is that anomalous diffusion occurs when the Central Limit Theorem (CLT) does not hold in its usual form. It is shown how simple arguments can be used to adapt the CLT to these situations, thereby allowing to predict the resulting behaviours. Physical examples, which can be relevant to e.g. flows in porous media, are analysed accordingly.