Generalization of Fluctuation-Dissipation Theorem to Systems with Absorbing States

TL;DR

This paper extends the fluctuation-dissipation theorem to systems with absorbing states, enabling accurate predictions of their response to perturbations even as they approach extinction, which standard theory cannot handle.

Contribution

The authors develop a new theoretical framework that generalizes the fluctuation-dissipation theorem for systems with absorbing states, applicable across various fields.

Findings

Successfully predicts effects of perturbations increasing extinction rates

Demonstrates applicability to ecological and biological systems

Reveals features of the path to extinction hidden by standard theories

Abstract

Systems that evolve towards a state from which they cannot depart are common in nature. But the fluctuation-dissipation theorem, a fundamental result in statistical mechanics, is mainly restricted to systems near-stationarity. In processes with absorbing states, the total probability decays with time, eventually reaching zero and rendering the predictions from the standard response theory invalid. In this article, we investigate how such processes respond to external perturbations and develop a new theory that extends the framework of the fluctuation-dissipation theorem. We apply our theory to two paradigmatic examples that span vastly different fields - a birth-death process in forest ecosystems and a targeted search on DNA by proteins. These systems can be affected by perturbations which increase their rate of extinction/absorption, even though the average or the variance of population sizes are left unmodified. These effects, which are not captured by the standard response theory, are exactly predicted by our framework. Our theoretical approach is general and applicable to any system with absorbing states. It can unveil important features of the path to extinction masked by standard approaches.