Temperature inversion in long-range interacting systems

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. This work is motivated by an attempt how such a counterintuitive effect may spontaneously arise in nonequilibrium states, unveiling its minimal ingredients and the underlying physical mechanism. We start with asking a simple yet physically relevant question: What happens if an isolated macroscopic system in thermal equilibrium is momentarily disturbed, e.g., by an impulsive force or a ``kick"? If the interactions among the system constituents are short-ranged, collisions redistribute the kick-injected energy among the particles, yielding a fast relaxation to a new equilibrium, with a Maxwellian velocity distribution and a uniform temperature across the system. Is the scenario the same if instead the interactions are long-ranged? For long-range systems, collisional effects act over a characteristic time that, unlike short-range systems, scales with the system size N, diverging when N goes to infinity. 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. We have shown that nonequilibrium stationary states with temperature inversions are the typical outcome of a
perturbation acting for a short time on a clustered equilibrium state of a long-range interacting system. This rather surprising result can be explained in terms of Landau damping and velocity filtration, suggesting that temperature inversions may occur whenever the dynamics is collisionless up to the relevant timescales. This mechanism may be actually relevant to understand temperature inversions observed in nature. This work was partially supported by CNPq and published in its complete version at Physical Review E (Rapid Communications) 92, 020101(R) (2015).