This work presents a theoretical framework for structural adaptation in closed nonlinear dynamical systems under strong external forcing. We consider a fully connected lattice of abstract discrete oscillators subject to a parametric energetic drive. Using a Kuramoto-like formulation, we show that unbounded energy growth can be avoided through an endogenous coarse-graining mechanism in which the effective macroscopic phase space temporarily expands. This dynamic expansion acts as an internal heat sink, reducing effective energy density and slowing local dynamics. As a result, the system undergoes a finite-time phase synchronization transition, leading to a significant reduction in relational entropy and the emergence of a coherent macroscopic state. The synchronized configuration is characterized by a collective frequency that imparts a mass-like effective inertia in a dynamical sense, associated with increased robustness against perturbations. These results provide a physically motivated perspective on self-organization, structural memory, and energy-to-structure conversion in closed non-equilibrium systems.
Claudia Attaianese (2026) studied this question.