Applying Fluctuation Dissipation Relations to Active Systems

Active systems are not invariant under time-reversal, and therefore do not obey the Fluctuation Dissipation Theorem. Recent work, applying Martin-Siggia-Rose path integral methods, has shown that correlation functions and linear response functions of active systems obey a family of more general Fluctuation Dissipation Relations. This is, in the most general case, a formal relationship. However, in specific models we find directly applicable identities—exact or using systematic approximations schemes such as perturbative field theory. We therefore consider a range of models—for example the Noisy Complex Ginzburg-Landau equation, models of odd mobility, the Non-Reciprocal Cahn-Hilliard—and illustrate how to apply Fluctuation Dissipation Relations in models far from equilibrium.