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

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.