  We consider the time evolution of nonequilibrium quantum scalar fields in the
O(N) model, using the next-to-leading order 1/N expansion of the 2PI effective
action. A comparison with exact numerical simulations in 1+1 dimensions in the
classical limit shows that the 1/N expansion gives quantitatively precise
results already for moderate values of N. For sufficiently high initial
occupation numbers the time evolution of quantum fields is shown to be
accurately described by classical physics. Eventually the correspondence breaks
down due to the difference between classical and quantum thermal equilibrium.
