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Out-of-equilibrium quasistationary states (QSSs) are one of the signatures ofa broken ergodicity in long-range interacting systems. For the widely studiedHamiltonian Mean-Field model, the lifetime of some QSSs has been shown todiverge with the number N of degrees of freedom with a puzzling N^1.7 scalinglaw, contradicting the otherwise widespread N scaling law. It is shown herethat this peculiar scaling arises from the locality properties of the dynamicscaptured through the computation of the diffusion coefficient in terms of theaction variable. The use of a mean first passage time approach proves to besuccessful in explaining the non-trivial scaling at stake here, and sheds somelight on another case, where lifetimes diverging as e^N above some criticalenergy have been reported.

Action diffusion and lifetimes of quasistationary states in the Hamiltonian Mean Field model