We develop a framework for obtaining rate coefficients in non-

linear kinetic equations for slowly evolving quantities in a non-

equilibrium system by matching real time correlation functions

of thermal fluctuations computed in an effective description to

those computed in thermal quantum field theory. We apply

this formalism to sterile neutrino occupancies and lepton minus

baryon numbers. 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. We apply

the formula for linear coefficients to the equilibration of right-

handed electrons in the symmetric phase of the Standard Model,

which happens relatively late in the history of the Universe due

to the smallness of the electron Yukawa coupling. We compute

the equilibration rate at leading order in the Standard Model

couplings by including gauge interactions, the top Yukawa- and

the Higgs self-interaction. The dominant contribution is due to

2 -> 2 particle scattering, even though the rate of (inverse) Higgs

decays is strongly enhanced by multiple soft scattering which is

included by Landau-Pomeranchuk-Migdal (LPM) resummation.

Our numerical result for the equilibration rate is substantially

larger than approximations presented in previous literature. We

find that the equilibration of right-handed electrons takes place at

temperatures at which also low-scale leptogenesis can be realized,

and we argue that in this case the two processes do not decouple.