# Anomalous diffusion: A basic mechanism for the evolution of inhomogeneous systems

## TL;DR

This paper reviews classical and recent results on anomalous diffusion, focusing on mechanisms and methods for analyzing diffusive regimes in inhomogeneous systems across physics, chemistry, and biology.

## Contribution

It introduces mechanisms and analytical methods for understanding anomalous diffusion in small-scale inhomogeneous systems, emphasizing memory functions, irreversibility, and ergodicity.

## Key findings

- Methods for analyzing diffusive regimes are applicable to systems from single molecules to biological cells.
- Anomalous diffusion mechanisms are fundamental in condensed matter, chemistry, and biology.
- The review highlights the importance of memory and ergodicity in diffusive processes.

## Abstract

In this article we review classical and recent results in anomalous diffusion and provide mechanisms useful for the study of the fundamentals of certain processes, mainly in condensed matter physics, chemistry and biology. Emphasis will be given to some methods applied in the analysis and characterization of diffusive regimes through the memory function, the mixing condition (or irreversibility), and ergodicity. Those methods can be used in the study of small-scale systems, ranging in size from single-molecule to particle clusters and including among others polymers, proteins, ion channels and biological cells, whose diffusive properties have received much attention lately.