Generalized hydrodynamics (GHD) was proposed recently as a formulation of
hydrodynamics for integrable systems, taking into account infinitely-many
conservation laws. In this note we further develop the theory in various
directions. By extending GHD to all commuting flows of the integrable model, we
provide a full description of how to take into account weakly varying force
fields, temperature fields and other inhomogeneous external fields within GHD.
We expect this can be used, for instance, to characterize the non-equilibrium
dynamics of one-dimensional Bose gases in trap potentials. We further show how
the equations of state at the core of GHD follow from the continuity relation
for entropy, and we show how to recover Euler-like equations and discuss
possible viscosity terms.