  Temperature inversions occur in nature, e.g., in the solar corona and in
interstellar molecular clouds: somewhat counterintuitively, denser parts of the
system are colder than dilute ones. We propose a simple and appealing way to
spontaneously generate temperature inversions in systems with long-range
interactions, by preparing them in inhomogeneous thermal equilibrium states and
then applying an impulsive perturbation. In similar situations, short-range
systems would typically relax to another thermal equilibrium, with uniform
temperature profile. By contrast, in long-range systems, the interplay between
wave-particle interaction and spatial inhomogeneity drives the system to
nonequilibrium stationary states that generically exhibit temperature
inversion. We demonstrate this mechanism in a simple mean-field model and in a
two-dimensional self-gravitating system. Our work underlines the crucial role
the range of interparticle interaction plays in determining the nature of
steady states out of thermal equilibrium.
