  We investigate the decoherence of histories of local densities for linear
oscillators models. It is shown that histories of local number, momentum and
energy density are approximately decoherent, when coarse-grained over
sufficiently large volumes. Decoherence arises directly from the proximity of
these variables to exactly conserved quantities (which are exactly decoherent),
and not from environmentally-induced decoherence. We discuss the approach to
local equilibrium and the subsequent emergence of hydrodynamic equations for
the local densities.
