  We study the large time dynamics of a macroscopically large quantum systems
under a sudden quench. We show that, first of all, for a generic system in the
thermodynamic limit the Gibbs distribution correctly captures the large time
dynamics of its global observables. In contrast, for an integrable system, the
generalized Gibbs ensemble captures its global large time dynamics only if the
system can be thought of as a number of noninteracting uncorrelated fermionic
degrees of freedom. The conditions for the generalized Gibbs ensemble to
capture the large time dynamics of local quantities are likely to be far less
restrictive, but this question is not systematically addressed here.
