  A new transient effective theory of the relativistic Boltzmann equation is
derived for locally momentum-anisotropic systems. In the expansion of the
distribution function around a local "quasi-equilibrium" state a
non-hydrodynamic dynamical degree of freedom is introduced at leading order
that breaks local momentum isotropy. By replacing the deviation of the
distribution function from this quasi-equilibrium state in terms of moments of
the leading-order distribution and applying a systematic power counting scheme
that orders the non-hydrodynamic modes by their microscopic time scales, a
closed set of equations for the dynamical degrees of freedom is obtained.
Truncating this set at the level of the slowest non-hydroynamic mode we find
that it exhibits transient oscillatory behavior -- a phenomenon previously
found only in strongly coupled theories, where it appears to be generic. In
weakly coupled systems described by the Boltzmann equation, these transient
oscillations depend on the breaking of local momentum isotropy being treated
non-perturbatively at leading order in the expansion of the distribution
function.
