Tsallis distributions, Lévy walks and correlated-type anomalous diffusion result from state-dependent diffusion

• Tsallis (qq-Gaussian) distributions are ubiquitous.
• The underlying dynamics have for the most part remained elusive.
• Fission–fusion processes lead to Tsallis distributions.
• Fission–fusion processes are common in systems described by Tsallis distributions.

We show that non-linear diffusion equations can describe state-dependent diffusion, i.e., fission–fusion dynamics. We thereby provide a new dynamical basis for understanding Tsallis distributions (qq-Gaussian distributions), anomalous diffusion (subdiffusion, superdiffusion and superballistic movements), Lévy walks and multiplicative noise. Our analyses find empirical support in the movements of single Hydra and kidney cells in cell aggregates. It may explain why Tsallis distributions characterise seemingly disparate phenomena including cell motility, inverse bremsstrahlung absorption, high-energy particle collisions, particle movements in granular matter and the re-association of heme-ligands in folded proteins. The common underlining factor is state-dependent diffusion.