Validity of relativistic hydrodynamics beyond local equilibrium

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 non-perturbative modes that encode initial conditions. The non-perturbative 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+1D Bjorken scenario, we demonstrate that the exact evolution of non-equilibrium 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+1D, 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 natural explanation for the remarkable success of hydrodynamics in modeling quark-gluon plasma evolution.