Thermodynamic constraints and exact scaling exponents of flocking matter

TL;DR

This paper derives exact scaling exponents for transport coefficients in polar active fluids by applying thermodynamic constraints and a formalism for boost-agnostic passive fluids, aligning theory with recent simulations and experiments.

Contribution

It introduces a thermodynamic approach to determine exact scaling exponents in flocking matter, connecting formalism with the Toner-Tu model and empirical data.

Findings

Exact scaling exponents match numerical simulations.

Thermodynamic constraints relate phenomenological parameters.

Transport coefficients follow specific power-law scalings.

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