A reduction scheme for coupled Brownian harmonic oscillators

We propose a reduction scheme for system constituted by two coupled harmonically-bound Brownian oscillators. reduce the description constructing lower dimensional model which inherits some of basic features original dynamics and is written in terms suitable transport coefficients. The proposed procedure twofold: while deterministic component obtained direct application invariant manifold method, diffusion are determined via Fluctuation-Dissipation Theorem. highlight behavior coefficients up to critical value coupling parameter, marks endpoint interval contracted available. study weak regime addressed commutativity alternative paths also discussed.