  The temperature of the solar atmosphere increases from thousands to millions
of degrees moving from the lower layer (chromosphere) to the outermost one
(corona), while the density drops accordingly. The mechanism behind this
phenomenon, known as a temperature inversion, is still unknown. In this work,
we model a coronal loop as a collisionless plasma confined in a semicircular
tube that is subject to the Sun's gravity and in thermal contact with a fully
collisional chromosphere behaving as a thermostat at the loop's feet. By using
kinetic $N$-particle simulations and analytical calculations, we show that
rapid, intermittent, and short-lived heating events in the chromosphere drive
the coronal plasma towards a non-equilibrium stationary state. The latter is
characterized by suprathermal tails in the particles' velocity distribution
functions, exhibiting temperature and density profiles strikingly similar to
those observed in the atmosphere of the Sun. These results suggest that a
million-Kelvin solar corona can be produced without the local deposition of
heat in the upper layer of the atmosphere that is typically assumed by standard
approaches. We find that suprathermal distribution functions in the corona are
self-consistently produced instead of postulated a priori, in contrast to
classical kinetic models based on a velocity filtration mechanism.
