Irreducible memory function for dissipative stochastic systems with detailed balance

We show quite generally that the memory function for purely dissipative stochastic systems with detailed balance can be reduced further and can be expressed in terms of the irreducible memory function. This generalizes the similar finding for the Smoluchowski equation. The irreducible memory function is intimately connected with the lifetime renormalization, and is shown to provide a useful starting point for introducing approximations such as the mode coupling approximation.