  The most general description of the classical world is in terms of local
densities (such as number, momentum, energy), and these typically evolve
according to evolution equations of hydrodynamic form. To explain the emergent
classicality of these variables from an underlying quantum theory, it is
therefore necessary to show, firstly, that these variables exhibit negligible
interference, and secondly, that the probabilities for histories of them are
peaked around hydrodynamic evolution. The implementation of this programme in
the context of the decoherent histories approach to quantum theory is
described. It is argued that, for a system of weakly interacting particles, the
eigenstates of local densities (averaged over a sufficiently large volume)
remain approximate eigenstates under time evolution. This is a consequence of
their close connection with the corresponding exactly conserved (and so exactly
decoherent) quantities. The subsequent derivation of hydrodynamic equations
from decoherent histories is discussed.
