Thermodynamic constraints and exact scaling exponents of flocking matter

Abstract

We use advances in the formalism of boost agnostic passive fluids to constrain transport in polar active fluids, which are subsequently described by the Toner-Tu equations. Acknowledging that the system fundamentally breaks boost symmetry we compel what were previously entirely phenomenological parameters in the Toner-Tu model to satisfy precise relationships among themselves. Consequently, we propose a thermodynamic argument to determine the exact scalings of the transport coefficients under dynamical renormalisation group flow. These scalings perfectly agree with the results of recent state-of-the-art numerical simulation and experiments