Fluid dynamics from the Boltzmann equation using a maximum entropy distribution

TL;DR

This paper introduces a maximum entropy-based macroscopic theory derived from the Boltzmann equation, capable of accurately modeling far-from-equilibrium fluid dynamics in heavy-ion collisions across different regimes.

Contribution

It develops a novel, comprehensive framework that incorporates all orders of dissipative effects, extending beyond traditional hydrodynamics and matching kinetic theory results.

Findings

Excellent agreement with kinetic theory in various flow regimes

Effective modeling of far-from-equilibrium dynamics

Handles large dissipative fluxes without truncation

Abstract

Using the recently developed ``Maximum Entropy'' (or ``least biased'') distribution function to truncate the moment hierarchy arising from kinetic theory, we formulate a far-from-equilibrium macroscopic theory that provides the possibility of describing both free-streaming and hydrodynamic regimes of heavy-ion collisions within a single framework. Unlike traditional hydrodynamic theories that include viscous corrections to finite order, the present formulation incorporates contributions to all orders in shear and bulk inverse Reynolds numbers, allowing it to handle large dissipative fluxes. By considering flow profiles relevant for heavy-ion collisions (Bjorken and Gubser flows), we demonstrate that the present approach provides excellent agreement with underlying kinetic theory throughout the fluid's evolution and, especially, in far-off-equilibrium regimes where traditional hydrodynamics breaks down.