We examine the applicability of relativistic hydrodynamics far from equilibrium by constructing formal solutions of the Boltzmann moment equations in the relaxation time approximation. These solutions naturally decompose into a divergent gradient series and exponentially decaying nonperturbative modes that encode initial conditions. The nonperturbative contributions are essential for understanding causality, the divergence of the gradient series, and the unexpected effectiveness of relativistic hydrodynamics far from equilibrium. In the $0+1\mathrm{D}$ Bjorken scenario, we demonstrate that the exact evolution of nonequilibrium terms shares the same structural form as the gradient expansion, differing only through modified transport coefficients that reflect both initial data and free-streaming dynamics. Extending to $3+1\mathrm{D}$, we find that hydrodynamics remains effective not because the system is close to equilibrium, but because it interpolates smoothly between free streaming and collective behavior. This perspective offers a possible explanation for the remarkable success of hydrodynamics in modeling quark-gluon plasma evolution.

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• Kinetic theory
• Quark-gluon plasma
• Relativistic heavy-ion collisions
• Transport in heavy-ion collisions
• Hydrodynamic models