  A popular aspect of black holes physics is the mathematical analogy between
their laws, coming from general relativity and the laws of thermodynamics. The
analogy is achieved by identifying a suitable set of observables, precisely:
\emph{(a)} $E=M$ (being $E$ the thermodynamic free energy and $M$ the mass of
the BH), \emph{(b)} $T=\alpha \kappa $ (with $T$ the absolute temperature,
$\kappa $ the so-called surface gravity on event horizon and $% \alpha $ a
suitable dimensional constant) and \emph{(c)} $S=(1/8\pi \alpha)A $ (where $S$
is the thermodynamic entropy of the black hole and $A$ the surface of the event
horizon). However, despite numerous investigations and efforts spent on the
subject, the theoretical foundations of such identifications between physical
quantities belonging to apparently unrelated frameworks are not yet clear. The
goal of this work is to provide the contribution to the black hole entropy,
coming from matter in the black hole exterior. 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.
