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Twenty three years ago, cosmological N-body simulations revealedquasi-universal NFW dark matter halos, whose physical origin is still unclear.This work tries to solve this issue by Landau-Ginzburg (LG) theory inequilibrium statistical mechanics. We replace the order parameter in LG theoryby density and consider the dark matter halos as fluctuations from theequilibrium state of the background, which can be the main halos for thesubhalos, or the homogeneous and isotropic Universe for the galaxy clusterhalos. With the assumption that the fluctuations of Helmholtz free energydepend mainly on the density and its gradient, which is shown to be consistentwith the behavior of the power spectrum near the cluster scale, we can easilyobtain the universal $r^{-1}$ cusp of the equilibrium dark matte halo withoutother requirements. This work strongly suggests that more studies should bedone for the self-gravitating systems by statistical mechanics.

Explaining the cuspy dark matter halo by Landau-Ginzburg theory