  DGLAP evolution equations may be presented in a form completely analogous to
the Boltzmann equation. This provides a natural proof of the positivity of the
spin-dependent parton distributions, provided the initial distributions at
$Q^2_0$ are also positive. In addition, the evolution to $Q^2 < Q^2_0$ may
violate positivity, providing therefore a 'time arrow'. The positivity
condition is just $|\Delta P_{ij} (z)| \leq P_{ij} (z) $ for $z < 1$ for all
types of partons, while the $'+'$prescription and terms containing
$\delta(1-z)$ do not affect positivity. This method allows one to complete
immediately the existing proof of Soffer inequality at leading and
next-to-leading order.
