  The generalized Gibbs ensemble has been shown to be relevant in the
relaxation of a completely integrable system subject to a quantum quench, in
the sense that it accurately predicts the steady values of some physical
variables. We proceed to further question its relevance by giving the quenched
system a second quench. The concern is whether the generalized Gibbs ensemble
can also accurately predict the relaxed system's response to the second quench.
Two case studies with the transverse Ising model and the hard-core bosons in
one dimension yield an affirmative answer. The relevance of the generalized
Gibbs ensemble in the non-equilibrium dynamics of integrable systems is then
greatly strengthened.
