Late Time Correlations in Hydrodynamics: Beyond Constitutive Relations

We investigate the effects of nonlinear stochastic interactions on hydrodynamic response functions. The interactions are parametrized by ``stochastic transport coefficients'' that are invisible in the classical constitutive relations, but nonetheless affect the late time hydrodynamic correlations. We present a classification scheme for such coefficients that applies beyond the naive stochastic hydrodynamics. Our results indicate that conventional transport coefficients do not provide a universal characterization of long-distance late time behavior of nonequilibrium thermal systems.