  Prompted by the relevant problem of temperature inversion (i.e. gradient of
density anti-correlated to the gradient of temperature) in astrophysics, we
introduce a novel method to model a gravitationally confined multi-component
collisionless plasma in contact with a fluctuating thermal boundary. We focus
on systems with anti-correlated (inverted) density and temperature profiles,
with applications to solar physics. The dynamics of the plasma is analytically
described via the coupling of an appropriated coarse-grained distribution
function and temporally coarse-grained Vlasov dynamics. We derive a stationary
solution of the system and predict the inverted density and temperature
profiles of the two-species for scenarios relevant for the corona. We validate
our method by comparing the analytical results with kinetic numerical
simulations of the plasma dynamics in the context of the two-species
Hamiltonian mean-field model (HMF). Finally, we apply our theoretical framework
to the problem of the temperature inversion in the solar corona obtaining
density and temperature profiles in remarkably good agreement with the
observations.
