  Using the recently developed ``Maximum Entropy'' (or ``least biased'')
distribution function to truncate the moment hierarchy arising from kinetic
theory, we formulate a far-from-equilibrium macroscopic theory that provides
the possibility of describing both free-streaming and hydrodynamic regimes of
heavy-ion collisions within a single framework. Unlike traditional hydrodynamic
theories that include viscous corrections to finite order, the present
formulation incorporates contributions to all orders in shear and bulk inverse
Reynolds numbers, allowing it to handle large dissipative fluxes. By
considering flow profiles relevant for heavy-ion collisions (Bjorken and Gubser
flows), we demonstrate that the present approach provides excellent agreement
with underlying kinetic theory throughout the fluid's evolution and,
especially, in far-off-equilibrium regimes where traditional hydrodynamics
breaks down.
