Non-equilibrium transitions in multiscale systems with a bifurcating slow manifold

Abstract

Noise-induced transitions between metastable fixed points in systems evolving on multiple time scales are analyzed in situations where the time scale separation gives rise to a slow manifold with bifurcation. This analysis is performed within the realm of large deviation theory. It is shown that these non-equilibrium transitions make use of a reaction channel created by the bifurcation structure of the slow manifold, leading to vastly increased transition rates. Several examples are used to illustrate these findings, including an insect outbreak model, a system modeling phase separation in the presence of evaporation, and a system modeling transitions in active matter self-assembly. The last example involves a spatially extended system modeled by a stochastic partial differential equation.

References in corpus (6)

• Motility-Induced Phase Separation
• Statistical Mechanics of Interacting Run-and-Tumble Bacteria
• Macroscopic fluctuation theory
• Scalar ${\varphi }^4$ field theory for active-particle phase separation
• Large Deviations in Fast-Slow Systems
• Non-classical large deviations for a noisy system with non-isolated attractors

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• Stochastic models of ventilation driven by opposing wind and buoyancy