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.
Generalized hydrodynamics in strongly interacting 1D Bose gases