Hydrodynamics without Boost-Invariance from Kinetic Theory: From Perfect Fluids to Active Flocks

TL;DR

This paper derives hydrodynamic equations for perfect fluids without boost invariance from kinetic theory, revealing how microscopic interactions influence macroscopic behavior in active flock systems.

Contribution

It introduces a kinetic theory framework for non-boost-invariant hydrodynamics, connecting microscopic interactions to macroscopic coefficients in active matter.

Findings

Identification of transport coefficients in non-boost-invariant hydrodynamics

Derivation of a drift term leading to equilibrium with the environment

Relation between microscopic interactions and hydrodynamic coefficients

Abstract

We derive the hydrodynamic equations of perfect fluids without boost invariance [1] from kinetic theory. Our approach is to follow the standard derivation of the Vlasov hierarchy based on an a-priori unknown collision functional satisfying certain axiomatic properties consistent with the absence of boost invariance. The kinetic theory treatment allows us to identify various transport coefficients in the hydrodynamic regime. We identify a drift term that effects a relaxation to an equilibrium where detailed balance with the environment with respect to momentum transfer is obtained. We then show how the derivative expansion of the hydrodynamics of flocks can be recovered from boost non-invariant kinetic theory and hydrodynamics. We identify how various coefficients of the former relate to a parameterization of the so-called equation of kinetic state that yields relations between different coefficients, arriving at a symmetry-based understanding as to why certain coefficients in hydrodynamic descriptions of active flocks are naturally of order one, and others, naturally small. When inter-particle forces are expressed in terms of a kinetic theory influence kernel, a coarse-graining scale and resulting derivative expansion emerge in the hydrodynamic limit, allowing us to derive diffusion terms as infrared-relevant operators distilling different parameterizations of microscopic interactions. We conclude by highlighting possible applications.