Histories of Local Densities Don't Interfere

In the context of the decoherent histories approach to quantum theory, it is shown that macroscopic states consisting of histories of local densities (number, momentum , energy) exhibit negligible interference. This follows from the close connection of the local densities with the corresponding exactly conserved (and so exactly decoherent) quantities, and also from the observation that the eigenstates of local densities (averaged over a sufficiently large volume) remain approximate eigenstates under time evolution. The result is relevant to the derivation of hydrodynamic equations from decoherent histories.