A minimal theoretical–computational model of persistence in non-equilibrium dynamical systems

Giorgio Corona

Chaos, Solitons & Fractals, 2026, vol. 209, issue P1

Abstract: Long-lived spatial structures are common in systems driven far from equilibrium, where dissipation, nonlinearity, and spatial coupling generate coherent patterns, metastable domains, and defect-mediated organization. Here we introduce a minimal theoretical–computational framework in which persistence is promoted from an a posteriori diagnostic to an explicit local field coupled to phase evolution. The model combines a phase field, a persistence field, a causal activation criterion with persistence-dependent thresholding, and finite-range non-local feedback sourced by topological defects. Numerical simulations in two and three spatial dimensions show the formation and stabilization of long-lived persistent domains and their correlation with defect-related observables. Control simulations further show that the activated regime survives replacement of the local double-well persistence landscape by a single-well confining potential. The framework therefore isolates a minimal mechanism by which persistence can act as a dynamical variable in history-dependent nonequilibrium organization.

Keywords: Emergent persistence; Phase coherence; Causal threshold; Non-equilibrium dynamics; Pattern formation; Statistical mechanics; Topological defects (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:209:y:2026:i:p1:s0960077926006053

DOI: 10.1016/j.chaos.2026.118464

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