  The time evolution of a finite fermion system towards statistical equilibrium
is investigated using analytical solutions of a nonlinear partial differential
equation that had been derived earlier from the Boltzmann collision term. The
solutions of this fermionic diffusion equation are rederived in closed form,
evaluated exactly for simplified initial conditions, and applied to hadron
systems at low energies in the MeV-range, as well as to quark systems at
relativistic energies in the TeV-range where antiparticle production is
abundant. Conservation laws for particle number including created
antiparticles, and for the energy are discussed.
