  We explore the energy and entropy transport as well as the lepton number
variation induced from the mixing between electron and sterile neutrinos with
keV mass in the supernova core. We develop a radial- and time-dependent
treatment of the sterile-electron neutrino mixing, by including ordinary matter
effects, reconversions between sterile and electron antineutrinos, as well as
the collisional production of sterile particles for the first time. The
dynamical feedback due to the production of sterile particles on the
composition and thermodynamic properties of the core only leads to major
implications for the supernova physics for large mixing angles ($\sin^2 2
\theta > 10^{-10}$). Our findings suggest that a self-consistent appraisal of
the electron-sterile conversion physics in the supernova core would relax the
bounds on the sterile neutrino mixing parameters reported in the literature for
mixing angles smaller than $10^{-6}$, leaving the parameter space of the mass
and mixing angles of sterile neutrinos relevant to dark matter searches
unconstrained by supernovae.
