Fluctuation Dissipation Relations for the Non-Reciprocal Cahn-Hilliard Model

Recent results demonstrate how deviations from equilibrium fluctuation–dissipation theorem can be quantified for active field theories by deriving exact fluctuations dissipation relations that involve the entropy production [M. K. Johnsrud and R. Golestanian, Phys. Rev. Res. 7, L032053 (2025)].Here we develop and employ diagrammatic tools to perform perturbative calculations for a paradigmatic active field theory, the Non-Reciprocal Cahn-Hilliard (NRCH) model. We obtain analytical results, which serve as an illustration of how to implement the recently developed framework to active field theories, and help to illuminate the specific non-equilibrium characteristics of the NRCH field theory.