  We argue that a particle language provides a conceptually simple framework
for the description of anomalous equilibration in isolated quantum systems. We
address this paradigm in the context of integrable models, which are those with
particles that are stable against decay. In particular, we demonstrate that a
complete description of equilibrium ensembles for interacting integrable models
requires a formulation built from the mode occupation numbers of the underlying
particle content, mirroring the case of non-interacting particles. This yields
an intuitive physical interpretation of generalized Gibbs ensembles, and
reconciles them with the microcanonical ensemble. We explain how previous
attempts to identify an appropriate ensemble overlooked an essential piece of
information, and provide explicit examples in the context of quantum quenches.
