Attractor of hydrodynamic attractors

Shile Chen; Shuzhe Shi

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arXiv · 2509.08864

Attractor of hydrodynamic attractors

Shile Chen·Shuzhe Shi

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Abstract

Understanding how hydrodynamics emerges rapidly in the medium produced by relativistic heavy-ion collisions remains a key theoretical challenge. While the attractor solution -- manifesting as a non-thermal fixed point during the early evolution stage -- offers a potential explanation, it does not fully account for how far-from-equilibrium systems quickly approach near-equilibrium states. In this Letter, we demonstrate that the attractor in a higher-order hydrodynamic theory converges to the same solution as a second-order theory before reaching the Navier--Stokes limit. This finding suggests that commonly used second-order hydrodynamic equations, provided they incorporate the correct transport coefficients, are adequate to approximate the system's behavior starting from an intermediate time -- even when using a higher-order theory that would be more suitable for describing the far-from-equilibrium evolution.

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Shile Chen, Shuzhe Shi. 2025-09-10. Attractor of hydrodynamic attractors. https://arxiv.org/abs/2509.08864

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