  We study the evolution of hydrodynamic and non-hydrodynamic moments of the
distribution function using anisotropic and third-order Chapman-Enskog
hydrodynamics for systems undergoing Bjorken and Gubser flows. The hydrodynamic
results are compared with the exact solution of the Boltzmann equation with a
collision term in relaxation time approximation. While the evolution of the
hydrodynamic moments of the distribution function (i.e. of the energy momentum
tensor) can be described with high accuracy by both hydrodynamic approximation
schemes, their description of the evolution of the entropy of the system is
much less precise. We attribute this to large contributions from
non-hydrodynamic modes coupling into the entropy evolution which are not well
captured by the hydrodynamic approximations. The differences between the exact
solution and the hydrodynamic approximations are larger for the third-order
Chapman-Enskog hydrodynamics than for anisotropic hydrodynamics, which
effectively resums some of the dissipative effects from anisotropic expansion
to all orders in the anisotropy, and are larger for Gubser flow than for
Bjorken flow. Overall, anisotropic hydrodynamics provides the most precise
macroscopic description for these highly anisotropically expanding systems.
