Equilibrium and nonequilibrium properties of systems with long-range interactions

Abstract

We briefly review some equilibrium and nonequilibrium properties of systems with long-range interactions. Such systems, which are characterized by a potential that weakly decays at large distances, have striking properties at equilibrium, like negative specific heat in the microcanonical ensemble, temperature jumps at first order phase transitions, broken ergodicity. Here, we mainly restrict our analysis to mean-field models, where particles globally interact with the same strength. We show that relaxation to equilibrium proceeds through quasi-stationary states whose duration increases with system size. We propose a theoretical explanation, based on Lynden-Bell's entropy, of this intriguing relaxation process. This allows to address problems related to nonequilibrium using an extension of standard equilibrium statistical mechanics. We discuss in some detail the example of the dynamics of the free electron laser, where the existence and features of quasi-stationary states is likely to be tested experimentally in the future. We conclude with some perspectives to study open problems and to find applications of these ideas to dipolar media.

8 pages, 14 figures, Procs. of STATPHYS23, to be published on EPJB

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Cited by in corpus (7)

• The world of long-range interactions: A bird's eye view
• Fractional Liouville Equation on Lattice Phase-Space
• Extended gaussian ensemble solution and tricritical points of a system with long-range interactions
• Large Lattice Fractional Fokker-Planck Equation
• Multicanonical entropy like-solution of statistical temperature weighted histogram analysis method (ST-WHAM)
• Ensemble in-equivalence in supernova matter within a simple model
• The extended gaussian ensemble and metastabilities in the Blume-Capel model