  A nonlinear diffusion equation is proposed to account for thermalization in
fermionic and bosonic systems through analytical solutions. For constant
transport coefficients, exact time-dependent solutions are derived through
nonlinear transformations, and the corresponding local equilibration times are
deduced. Fermi-Dirac and Bose-Einstein distributions emerge as stationary
solutions of the nonlinear equation. As examples, local thermalization of
quarks and gluons in relativistic heavy-ion collisions, and of ultracold atoms
including time-dependent Bose-Einstein condensate formation are discussed.
