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Towards a fluid-dynamic description of an entire heavy-ion collision: from the colliding nuclei to the quark-gluon plasma phase

Andreas Kirchner, Federica Capellino, Eduardo Grossi, Stefan Floerchinger

TL;DR

The paper investigates whether the soft sector of heavy-ion collisions can be captured by a fully fluid-dynamical description from pre-collision to the quark-gluon plasma, using Landau matching to initialize the system and an EOS spanning the QCD phase diagram. It employs a second-order viscous hydrodynamics framework (Israel–Stewart–Müller) to model relaxation toward equilibrium and analyzes an interactionless limit to gauge overlap dynamics, all while focusing on entropy production as a diagnostic. A simplified, isotropic Hubble-like contraction/expansion model demonstrates how entropy production—driven by viscosity and relaxation times—sets the final temperature, illustrating that transport properties can control key features of the evolution. The work lays foundational steps toward a dynamical description where the remaining uncertainties reside in QCD thermodynamics and transport coefficients, with plans to extend to higher-dimensional simulations and integrate more realistic EOS inputs.

Abstract

The fluid-dynamical modeling of a nuclear collision at high energy usually starts shortly after the collision. A major source of uncertainty comes from the detailed modeling of the initial state. While the collision itself likely involves far-from-equilibrium dynamics, it is not excluded that a fluid theory of second order can reasonably well describe its soft features. Here we explore this possibility and discuss how the state before the collision can be described in that setup, examine the required fluid-dynamical equations of motion and study the resulting entropy production. While we do here only first steps, we outline a larger program, which could lead to a dynamical description of heavy-ion collisions where the only uncertainty lies in the thermodynamic and transport properties of quantum chromodynamics.

Towards a fluid-dynamic description of an entire heavy-ion collision: from the colliding nuclei to the quark-gluon plasma phase

TL;DR

The paper investigates whether the soft sector of heavy-ion collisions can be captured by a fully fluid-dynamical description from pre-collision to the quark-gluon plasma, using Landau matching to initialize the system and an EOS spanning the QCD phase diagram. It employs a second-order viscous hydrodynamics framework (Israel–Stewart–Müller) to model relaxation toward equilibrium and analyzes an interactionless limit to gauge overlap dynamics, all while focusing on entropy production as a diagnostic. A simplified, isotropic Hubble-like contraction/expansion model demonstrates how entropy production—driven by viscosity and relaxation times—sets the final temperature, illustrating that transport properties can control key features of the evolution. The work lays foundational steps toward a dynamical description where the remaining uncertainties reside in QCD thermodynamics and transport coefficients, with plans to extend to higher-dimensional simulations and integrate more realistic EOS inputs.

Abstract

The fluid-dynamical modeling of a nuclear collision at high energy usually starts shortly after the collision. A major source of uncertainty comes from the detailed modeling of the initial state. While the collision itself likely involves far-from-equilibrium dynamics, it is not excluded that a fluid theory of second order can reasonably well describe its soft features. Here we explore this possibility and discuss how the state before the collision can be described in that setup, examine the required fluid-dynamical equations of motion and study the resulting entropy production. While we do here only first steps, we outline a larger program, which could lead to a dynamical description of heavy-ion collisions where the only uncertainty lies in the thermodynamic and transport properties of quantum chromodynamics.

Paper Structure

This paper contains 6 sections, 4 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Nuclei as static fluids
  3. Interactionless collision
  4. Fluid dynamics & equation of state
  5. Model system & results
  6. Conclusion

Figures (2)

  • Figure 1: Number density (left) and pressure (right) for different times obtained from the Landau matching procedure in the interactionless limit. The large densities and viscous corrections require a careful treatment of the fluid-dynamical equations and their numerical implementation.
  • Figure 2: Fluid field evolution during the contraction and expansion (left) and final temperature as function of the viscosity (right). The system is initialized at zero temperature at the phase transition and ends its evolution with a finite temperature due to the produced entropy and heat.