  We use a semiclassical approach to study out of equilibrium dynamics and
transport in quantum systems with massive quasiparticle excitations having
internal quantum numbers. In the universal limit of low energy quasiparticles,
the system is described in terms of a classical gas of colored hard-core
particles. Starting from an inhomogeneous initial state, in this limit we give
analytic expressions for the space and time dependent spin density and spin
current profiles. Depending on the initial state, the spin transport is found
to be ballistic or diffusive. In the ballistic case we identify a `second
front' that moves more slowly than the maximal quasiparticle velocity. Our
analytic results also capture the diffusive broadening of this ballistically
propagating front. To go beyond the universal limit, we study the effect of
non-trivial scattering processes in the $O(3)$ non-linear sigma model by
performing Monte Carlo simulations, and observe local equilibration around the
second front in terms of the densities of the particle species.
