Conserved moments in nonequilibrium field dynamics

We demonstrate with the example of Cahn-Hilliard dynamics that the macroscopic kinetics of first-order phase transitions exhibits an infinite number of constants of motion. Moreover, this results holds in any space dimension for a broad class of nonequilibrium processes whose macroscopic behavior is governed by equations of the form ∂φ/∂t = LW(φ), where φ is an open-quotes order parameter,close quotes W is an arbitrary function of φ, and L is a linear Hermitian operator. We speculate on the implications of this result