Exploring the applicability of dissipative fluid dynamics to small systems by comparison to the Boltzmann equation

TL;DR

This study compares relativistic fluid dynamics with Boltzmann equation solutions to assess the applicability of fluid models in small systems like p+p and p+A collisions, revealing surprising agreement even in regimes where fluid dynamics is expected to fail.

Contribution

It provides a systematic comparison between fluid dynamics and kinetic theory for small systems, highlighting the conditions under which fluid models remain valid.

Findings

Fair agreement in energy and particle density profiles.

Shear-stress tensor components are highly sensitive to implementation details.

Fluid dynamics matches transport theory even at high Knudsen and inverse Reynolds numbers.

Abstract

[Background] Experimental data from heavy-ion experiments at RHIC-BNL and LHC-CERN are quantitatively described using relativistic fluid dynamics. Even p+A and p+p collisions show signs of collective behavior describable in the same manner. Nevertheless, small system sizes and large gradients strain the limits of applicability of fluid-dynamical methods. [Purpose] The range of applicability of fluid dynamics for the description of the collective behavior, and in particular of the elliptic flow, of small systems needs to be explored. [Method] Results of relativistic fluid-dynamical simulations are compared with solutions of the Boltzmann equation in a longitudinally boost-invariant picture. As initial condition, several different transverse energy-density profiles for equilibrated matter are investigated. [Results] While there is overall a fair agreement of energy- and particle-density profiles, components of the shear-stress tensor are more sensitive to details of the implementation. The highest sensitivity is exhibited by quantities influenced by properties of the medium at freeze-out. [Conclusions] For some quantities, like the shear-stress tensor, agreement between fluid dynamics and transport theory extends into regions of Knudsen numbers and inverse Reynolds numbers where relativistic fluid dynamics is believed to fail.