Snap, Crackle, and Pop: This is why the potential of mean force clashes with the fluctuation dissipation relation

TL;DR

This paper investigates how thermodynamic forces in the generalized Langevin equation cause non-stationary fluctuations, challenging standard coarse-graining methods and emphasizing careful modeling of thermodynamic driving forces.

Contribution

It reveals that thermodynamic forces induce non-stationarity in fluctuations, affecting coarse-graining and modeling approaches in equilibrium systems.

Findings

Thermodynamic forces lead to non-stationary auto-correlation functions.

Standard coarse-graining can produce incompatible waiting-time distributions.

Care is needed when incorporating thermodynamic forces into Langevin equations.

Abstract

We analyze the non-linear generalized Langevin equation which contains a thermodynamic force. We show that even for systems in thermal equilibrium the presence of the thermodynamic force implies that the auto-correlation function of the fluctuating force becomes non-stationary. We further illustrate that a standard coarse-graining procedure that neglects this fact predicts waiting-time distributions incompatible with the original, microscopic process. We conclude that one needs to proceed with care when adding thermodynamic driving forces to the Langevin equation.