Dissipation functions and Brownian oscillators

TL;DR

This paper introduces a response theory framework for diffusion processes using Dissipation Functions, deriving exact formulas for Brownian oscillators and exploring model reduction in response analysis.

Contribution

It presents a novel general framework for response theory in diffusion processes and provides exact response formulas for Brownian oscillators.

Findings

Exact response formulas for overdamped and underdamped Brownian oscillators.

Model reduction and response formula extraction commute under certain conditions.

Framework applicable to a broad class of diffusion processes.

Abstract

We develop a general framework for response theory in diffusion processes governed by Fokker-Planck equations, based on the notion of the Dissipation Function. Using the analytically solvable Brownian oscillator model, we derive exact response formulae for both overdamped and underdamped dynamics of harmonically bound Brownian particles. We also demonstrate that for certain observables and under suitable time scaling, the operations of model reduction and response formula extraction commute.