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In the Hamiltonian mean-field model, we study the core-halo structure oflow-energy quasi-stationary states under unsteady water-bag type initialconditions. The core-halo structure results in the superposition of twoindependent Lynden-Bell distributions. We examine the completeness of theLynden-Bell relaxation and the relaxation between these two Lynden-Belldistributions.

Double Lynden-Bell Structure of Low-Energy Quasi-Stationary Distributions in the Hamiltonian Mean-Field Model