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This paper introduces a nonequilibrium instanton framework to efficiently compute transition rates between metastable spatial patterns in reaction-diffusion systems. The framework reveals that an effective entropy in path space significantly impacts pattern stability at finite particle numbers by increasing the exit rates of metastable patterns. The work demonstrates path entropy as a key organizing principle for nonequilibrium pattern formation, overcoming limitations of continuum mean-field descriptions and computational costs of exact stochastic simulations.
Path entropy, not just thermodynamics, dictates the stability of patterns in reaction-diffusion systems, offering a new lens for understanding nonequilibrium dynamics.
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.
BAIR