Thermodynamic constraints and exact scaling exponents of flocking matter

https://arxiv.org/abs/2405.02283

Flocking birds, robot swarms and bacterial colonies all represent a special type of matter termed "active matter". It is helpful to think of these swarms of particles carrying internal batteries from which they can draw energy and momentum as they move. A classical simplified model of a type of active matter is the Vicsek model. It describes some of the features of herds; importantly, the appearance of ordered states in two dimensions (which is otherwise forbidden).

The Toner-Tu model is an effective description of the Vicsek model in terms of hydrodynamic like fields. Importantly, to account for the symmetry breaking, the "momentum" equation contains a source term. Thus the theory is quasihydrodynamic.

As the field of boost agnostic hydrodynamics had not been developed until recently, many of the transport coefficients in the Toner-Tu model were treated as phenomenological parameters. I showed that if one assumes the existence of a generating functional for these fluids, then parameters are in fact constrained by relations between one another. Moreover I demonstrated that not only was the consistent with observations from numerical simulations (the existence of two speeds parallel and transverse to the order breaking parameter) but under the dynamical renormalisation group, my model predicted the observed scalings.