  We obtain non-linear kinetic equations for sterile neutrino occupancies and
lepton minus baryon numbers by matching real time correlation functions of
thermal fluctuations computed in an effective description to those computed in
thermal quantum field theory. After expanding in the sterile-neutrino Yukawa
couplings, the coefficients in the equations are written as real time
correlation functions of Standard Model operators. Our kinetic equations are
valid for an arbitrary number of sterile neutrinos of any mass spectrum. They
can be used to describe, e.g., low-scale leptogenesis via neutrino
oscillations, or sterile neutrino dark matter production in the Higgs phase.
