We calculate the entropy produced in the decoherence of a classical field
configuration and compare it with the entropy of a fully thermalized state with
the same energy. We find that decoherence alone accounts for a large fraction
of the equilibrium entropy when each field mode is only moderately occupied. We
apply this to theories of relativistic heavy ion collisions, which describe the
initial state as a collection of coherent color fields. Our results suggest
that decoherence may partly explain the rapid formation of a high entropy state
in these collisions.