  Integrable systems do not obey the strong eigenstate thermalization
hypothesis (ETH), which has been proposed as a mechanism of thermalization in
isolated quantum systems. It has been suggested that an integrable system
reaches a steady state described by a generalized Gibbs ensemble (GGE) instead
of thermal equilibrium. We prove that a generalized version of the strong ETH
holds for noninteracting integrable systems with translation invariance. Our
generalized ETH states that any pair of energy eigenstates with similar values
of local conserved quantities looks similar with respect to local observables,
such as local correlations. This result tells us that an integrable system
relaxes to a GGE for any initial state that has subextensive fluctuations of
macroscopic local conserved quantities. Contrary to the previous derivations of
the GGE, it is not necessary to assume the cluster decomposition property for
an initial state.
