  The open dynamics of quantum many-body systems involve not only the exchange
of energy, but also of other conserved quantities, such as momentum. This leads
to additional decoherence, which may have a profound impact in the dynamics.
Motivated by this, we consider a many-body system subject to total momentum
dephasing and show that under very general conditions this leads to a diffusive
component in the dynamics of any local density, even far from equilibrium. Such
component will usually have an intricate interplay with the unitary dynamics.
To illustrate this, we consider the case of a superfluid and show that momentum
dephasing introduces a damping in the sound-wave dispersion relation, similar
to that predicted by the Navier-Stokes equation for ordinary fluids. Finally,
we also study the effects of dephasing in linear response, and show that it
leads to a universal additive contribution to the diffusion constant, which can
be obtained from a Kubo formula.
