Kinetic Theory of Carroll Hydrodynamics

TL;DR

This paper develops a microscopic statistical mechanics framework for Carrollian fluids, deriving their equations and thermodynamics from first principles using a system of interacting branes.

Contribution

It introduces the first microscopic derivation of Carrollian fluid equations and thermodynamics based on a Carrollian analogue of Boltzmann's statistical approach.

Findings

Derived Carrollian fluid equations from microscopic principles.

Formulated initial elements of Carrollian thermodynamics.

Established a Carrollian analogue to the Boltzmann gas model.

Abstract

We develop the foundations of Carrollian statistical mechanics by considering a system of interacting instantonic space-filling branes on a flat background, thereby providing the closest Carrollian analogue to the Galilean gas of interacting particles that underpins Boltzmann's collision theory. By adapting Boltzmann's statistical approach within this framework, we provide a first-principles microscopic derivation of the so-called Carrollian fluid equations, which were previously obtained as the vanishing-speed-of-light limit of relativistic conservation laws. We then use this analysis as a basis for formulating the first elements of Carrollian thermodynamics.