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 nonthermal 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 focus on systems that are boost invariant and homogeneous in the transverse plane and 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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• Quark-gluon plasma
• Relativistic heavy-ion collisions
• Relativistic hydrodynamics