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We investigate the long-term relaxation of one-dimensional (${1D}$)self-gravitating systems, using both kinetic theory and $N$-body simulations.We consider thermal and Plummer equilibria, with and without collectiveeffects. All combinations are found to be in clear agreement with respect tothe Balescu-Lenard and Landau predictions for the diffusion coefficients.Interestingly, collective effects reduce the diffusion by a factor ${\sim 10}$.The predicted flux for Plummer equilibrium matches the measured one, which is aremarkable validation of kinetic theory. We also report on a situation of quasikinetic blocking for the same equilibrium.

Long-term relaxation of ${1D}$ self-gravitating systems