H-theorem for classical matter around a black hole
  We propose a classical solution for the kinetic description of matter falling into a black hole, which permits to evaluate both the kinetic entropy and the entropy production rate of classical infalling matter at the event horizon. The formulation is based on a relativistic kinetic description for classical particles in the presence of an event horizon. An H-theorem is established which holds for arbitrary models of black holes and is valid also in the presence of contracting event horizons. 
Piero Nicolini (Turin Polytechnic & Trieste U. & INFN, Trieste) and   Massimo Tessarotto (Trieste U. & CMFD, Trieste)