Mode-coupling theory and the fluctuation–dissipation theorem for nonlinear Langevin equations with multiplicative noise

In this letter, we develop a mode-coupling theory for a class of nonlinear Langevin equations with multiplicative noise using a field-theoretic formalism. These equations are simplified models of realistic colloidal suspensions. We prove that the derived equations are consistent with the fluctuation–dissipation theorem. We also discuss the generalization of the result given here to real fluids, and the possible description of supercooled fluids in the ageing regime. We demonstrate that the standard idealized mode-coupling theory is not consistent with the FDT in a strict field-theoretic sense.