  We consider the time evolution after sudden quenches of global parameters in
translational invariant Hamiltonians and study the time average expectation
values and entanglement entropies in finite chains. We show that in
noninteracting models the time average of spin correlation functions is
asymptotically equal to the infinite time limit in the infinite chain, which is
known to be described by a generalized Gibbs ensemble. The equivalence breaks
down considering nonlocal operators, and we establish that this can be traced
back to the existence of conservation laws common to the Hamiltonian before and
after the quench. We develop a method to compute the leading finite-size
correction for time average correlation functions and entanglement entropies.
We find that large corrections are generally associated to observables with
slow relaxation dynamics.
