CONSERVED MOMENTS IN NONEQUILIBRIUM FIELD-DYNAMICS

We demonstrate with the example of Cahn-Hilliard dynamics that the mac roscopic kinetics of first-order phase transitions exhibits an infinit e number of constants of motion. Moreover, this result holds in any sp ace dimension for a broad class of nonequilibrium processes whose macr oscopic behavior is governed by equations of the form partial-derivati vephi/partial-derivativet = LW(phi), where phi is an ''order parameter ,'' W is an arbitrary function of phi, and L is a linear Hermitian ope rator. We speculate on the implications of this result.