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 rôle the range of interparticle interaction plays in determining the nature of steady states out of thermal equilibrium. Stationary states far from thermal equilibrium occur in nature. In some cases, e.g., in the solar corona and in interstellar molecular clouds, such states exhibit temperature inversion: denser parts of the system are colder than dilute ones. This work is motivated by an attempt to explain how such a counterintuitive effect may spontaneously arise in nonequilibrium states, unveiling its minimal ingredients and the underlying physical mechanism. To this end, 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 shortranged, 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 [1]? For long-range systems, collisional effects act over a characteristic time τ coll that, unlike shortrange systems, scales with the system size N , diverging as N → ∞ [2]. As a result, a macroscopic system with longrange interactions starting from generic initial conditions will attain thermal equilibrium only after extremely long times, often exceeding typical observation times. Examples of long-range systems are self-gravitating systems, for which, e.g., τ coll ≃ 10 10 years for globular clusters and orders of magnitude larger than the age of the universe * tarcisio.nteles@gmail.com; S. Gupta and T. N. Teles contributed equally to the work. † shamikg1@gmail.com ‡ pierfrancesco.dicintio@unifi.it § lapo.casetti@unifi.it for galaxies [3,4]. The collisionless evolution of longrange interacting systems for times shorter than τ coll is governed by the Vlasov (or collisionless Boltzmann) equation [2]. When kicked out of thermal equilibrium, a longrange interacting system relaxes to a Vlasov-stationary state, and thermal eq...

We investigate thermal conduction in arrays of long-range interacting rotors and Fermi-Pasta-Ulam (FPU) oscillators coupled to two reservoirs at different temperatures. The strength of the interaction between two lattice sites decays as a power α of the inverse of their distance. We point out the necessity of distinguishing between energy flows towards or from the reservoirs and those within the system. We show that energy flow between the reservoirs occurs via a direct transfer induced by long-range couplings and a diffusive process through the chain. To this aim, we introduce a decomposition of the steady-state heat current that explicitly accounts for such direct transfer of energy between the reservoir. For 0≤α<1, the direct transfer term dominates, meaning that the system can be effectively described as a set of oscillators each interacting with the thermal baths. Also, the heat current exchanged with the reservoirs depends on the size of the thermalized regions: In the case in which such size is proportional to the system size N, the stationary current is independent on N. For α>1, heat transport mostly occurs through diffusion along the chain: For the rotors transport is normal, while for FPU the data are compatible with an anomalous diffusion, possibly with an α-dependent characteristic exponent.

By means of hybrid multiparticle collsion-particle-in-cell (MPC-PIC) simulations we study the dynamical scaling of energy and density correlations at equilibrium in moderately coupled two-dimensional (2D) and quasi-one-dimensional (1D) plasmas. We find that the predictions of nonlinear fluctuating hydrodynamics for the structure factors of density and energy fluctuations in 1D systems with three global conservation laws hold true also for 2D systems that are more extended along one of the two spatial dimensions. Moreover, from the analysis of the equilibrium energy correlators and density structure factors of both 1D and 2D neutral plasmas, we find that neglecting the contribution of the fluctuations of the vanishing self-consistent electrostatic fields overestimates the interval of frequencies over which the anomalous transport is observed. Such violations of the expected scaling in the currents correlation are found in different regimes, hindering the observation of the asymptotic scaling predicted by the theory.