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.