Hydrodynamics of Active Lévy Matter

Collective ordered motion is often modeled within the framework of active fluids, where hydrodynamic descriptions typically rely on microscopic models of active self-propelled particles subjected to alignment interactions and reorientational dynamics. However, single-particle superdiffusion is also widespread in biology as it can represent an optimal search strategy for living organisms. Nevertheless, the collective properties of interacting systems exhibiting such anomalous diffusive dynamics -- denoted here as active Lévy matter -- cannot be captured by current active fluid theories. Here, we formulate the hydrodynamic description of active Lévy matter by coarse-graining a microscopic model of alignment interacting active particles performing superdiffusion manifest as Lévy flights. This theory predicts characteristic disordered and ordered phases. Linear stability analysis suggests that the phase transition can be critical. This analysis highlights the need for more realistic models of active matter integrating both anomalous diffusive motility and inter-particle interactions and suggests that these models can shed new light on the universal properties of active systems.