  We elucidate the intermediate of the macroscopic fluid model and the
microscopic kinetic model by studying the Poisson algebraic structure of the
one-dimensional Vlasov-Poisson system. The water-bag model helps formulating
the hierarchy of sub-algebras, which interpolates the gap between the fluid and
kinetic models. By analyzing the embedding of the sub-manifold of an
intermediate hierarchy in a more microscopic hierarchy, we characterize the
microscopic effect as the symmetry breaking pertinent to a macroscopic
invariant.
