Abstract
 
 
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 try to understand which are the minimal ingredients and the basic physical mechanism behind such phenomena. We suggest that temperature inversions may spontaneously occur in a generic system with long-range interactions that is prepared in an inhomogeneous thermal equilibrium state and then brought out of equilibrium by 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 nonuniform temperature profiles with temperature inversion. This shows how crucial the role played by the range of interparticle interactions is in determining the nature of steady states attained when macroscopic systems are brought out of thermal equilibrium.