Long-term memory induced correction to Arrhenius law

TL;DR

This paper analytically demonstrates how long-term memory in non-Markovian processes causes a significant correction to Arrhenius law, affecting the kinetics of rare events in complex systems.

Contribution

It introduces a minimal Gaussian model to quantify the impact of long-term memory on rare event kinetics, revealing a correction to Arrhenius law with a second effective energy barrier.

Findings

Long-term memory induces a correction to Arrhenius law.

The correction manifests as a second effective energy barrier.

Memory effects depend on initial conditions.

Abstract

The Kramers escape problem is a paradigmatic model for the kinetics of rare events, which are usually characterized by Arrhenius law. So far, analytical approaches have failed to capture the kinetics of rare events in the important case of non-Markovian processes with long-term memory, as occurs in the context of reactions involving proteins, long polymers, or strongly viscoelastic fluids. Here, based on a minimal model of non-Markovian Gaussian process with long-term memory, we determine quantitatively the mean FPT to a rare configuration and provide its asymptotics in the limit of a large energy barrier $E$. Our analysis unveils a correction to Arrhenius law, induced by long-term memory, which we determine analytically. This correction, which we show can be quantitatively significant, takes the form of a second effective energy barrier $E'<E$ and captures the dependence of rare event kinetics on initial conditions, which is a hallmark of long-term memory. Altogether, our results quantify the impact of long-term memory on rare event kinetics, beyond Arrhenius law.