  Local kinetic equilibration is a prerequisite for hydrodynamics to be valid.
Here it is described through a nonlinear diffusion equation for finite systems
of fermions and bosons. The model is solved exactly for constant transport
coefficients in both cases. It has the proper Fermi-Dirac and Bose-Einstein
equilibrium limits and can replace the relaxation-time approximation (RTA). The
microscopic transport coefficients are determined through the macroscopic
variables temperature and local equilibration time. Applications to the
transverse energy of quarks and gluons in the initial stages of central
relativistic heavy-ion collisions, and to bosonic and fermionic atoms at low
energies appropriate for cold quantum gases are discussed.
