  For the Bjorken flow we investigate the hydrodynamization of different modes
of the one-particle distribution function by analyzing its relativistic kinetic
equations. We calculate the constitutive relations of each mode written as a
multi-parameter trans-series encoding the non-perturbative dissipative
contributions quantified by the Knudsen $Kn$ and inverse Reynolds $Re^{-1}$
numbers. At any given order in the asymptotic expansion of each mode, the
transport coefficients get effectively renormalized by summing over all
non-perturbative sectors appearing in the trans-series. This gives an effective
description of the transport coefficients that provides a new renormalization
scheme with an associated renormalization group equation, going beyond the
realms of linear response theory. As a result, the renormalized transport
coefficients feature a transition to their equilibrium fixed point, which is a
neat diagnostics of transient non-Newtonian behavior. As a proof of principle,
we verify the predictions of the effective theory with the numerical solutions
of their corresponding evolution equations. Our studies strongly suggest that
the phenomenological success of fluid dynamics far from local thermal
equilibrium is due to the transient rheological behavior of the fluid.
