  We study, both analytically and numerically, the Boltzmann transport equation
for the Hubbard chain with nearest neighbor hopping and spatially homogeneous
initial condition. The time-dependent Wigner function is matrix-valued because
of spin. The H-theorem holds. The nearest neighbor chain is integrable which,
on the kinetic level, is reflected by infinitely many additional conservation
laws and linked to the fact that there are also non-thermal stationary states.
We characterize all stationary solutions. Numerically, we observe an
exponentially fast convergence to stationarity and investigate the convergence
rate in dependence on the initial conditions.
