The Boltzmann Equation in Classical Yang-Mills Theory
  We give a detailed derivation of the Boltzmann equation, and in particular its collision integral, in classical field theory. We first carry this out in a scalar theory with both cubic and quartic interactions and subsequently in a Yang-Mills theory. Our method is not relied on a doubling of the fields, rather it is based on a diagrammatic approach representing the classical solution to the problem. 
V. Mathieu, A. H. Mueller, D. N. Triantafyllopoulos
hep-ph hep-th