Pattern stability in reaction-diffusion systems depends on path entropy

TL;DR

This paper introduces a nonequilibrium instanton framework to analyze how path entropy influences the stability of patterns in reaction-diffusion systems far from equilibrium, especially at finite particle numbers.

Contribution

It develops a novel theoretical approach to efficiently compute transition rates between patterns and reveals the role of path entropy in pattern stability.

Findings

Path entropy can significantly alter pattern stability.

The instanton framework enables efficient transition rate calculations.

Path entropy acts as an organizing principle in nonequilibrium pattern formation.

Abstract

Reaction-diffusion systems driven far from thermodynamic equilibrium through the injection of energy can support multiple distinct spatial patterns that persist as long-lived dynamical phases. The stability of these metastable phases is not determined by thermodynamics, but by the transition paths connecting them. At finite particle numbers, intrinsic stochasticity induces rare transitions between competing patterns, rendering continuum mean-field descriptions insufficient, while exact stochastic simulations become computationally prohibitive in spatially extended systems. Here, we develop a nonequilibrium instanton framework that enables efficient computation of transition rates between metastable patterns from a single optimal transition path and its fluctuations. Using this theoretical framework, we show that an effective entropy in path space can qualitatively alter stability at finite particle numbers by increasing the exit rates of metastable patterns. By studying models of varying complexity, this work establishes path entropy as a key organizing principle for nonequilibrium pattern formation.