  The far-from-equilibrium dynamics of an ultracold, one-dimensional Bose gas
is studied. The focus is set on the comparison between the solutions of fully
dynamical evolution equations derived from the 2PI effective action and their
corresponding kinetic approximation in the form of Boltzmann-type transport
equations. It is shown that during the time evolution of the gas a kinetic
description which includes non-Markovian memory effects in a gradient expansion
becomes valid. The time scale at which this occurs is shown to exceed
significantly the time scale at which the system's evolution enters a
near-equilibrium drift period where a fluctuation dissipation relation is found
to hold and which would seem to be predestined for the kinetic approximation.
