The Fluctuation–Dissipation Theorem Revisited: Beyond the Gaussian Approximation

Abstract

A linear response theory of systems of interest in atmospheric and climate dynamics taking fully into account the nonlinearities of the underlying processes is developed. Under the assumption that the source of intrinsic variability can be modeled as a white-noise process, a Fokker–Planck equation approach leads to fluctuation–dissipation-type expressions in the form of time cross-correlation functions, linking the perturbation-induced shift of an observable to the statistical and dynamical properties of the reference system. These expressions feature a generalized potential function and enable one to go systematically beyond the Gaussian approximation usually adopted in the literature. Full solutions and explicit expressions are derived for different subclasses of systems, including a global climate model giving rise to oscillatory behavior.