  Locally quasi-stationary states (LQSS) were introduced as inhomogeneous
generalisations of stationary states in integrable systems. Roughly speaking,
LQSSs look like stationary states, but only locally. Despite their key role in
hydrodynamic descriptions, an unambiguous definition of LQSSs was not given. By
solving the dynamics in inhomogeneous noninteracting spin chains, we identify
the set of LQSSs as a subspace that is invariant under time evolution, and we
explicitly construct the latter in a generalised XY model. As a by-product, we
exhibit an exact generalised hydrodynamic theory (including "quantum
corrections").
