  We explore the far-off-equilibrium aspects of the (1+1)-dimensional
early-stage evolution of a weakly-coupled quark-gluon plasma using kinetic
theory and hydrodynamics. For a large set of far-off-equilibrium initial
conditions the system exhibits a peculiar phenomenon where its total
equilibrium entropy decreases with time. Using a non-equilibrium definition of
entropy based on Boltzmann's H-function, we demonstrate how this apparently
anomalous behavior is consistent with the second law of thermodynamics. We also
use the H-function to formulate `maximum-entropy' hydrodynamics, a
far-off-equilibrium macroscopic theory that can describe both free-streaming
and near-equilibrium regimes of quark-gluon plasma in a single framework.
