Entropy-Gated Wave Control for Identity Preservation in Adaptive Systems

We introduce an entropy-gated wave control framework for adaptive dynamical systems in which dissipation is activated only when an information-theoretic identity invariant is violated. The model couples a second-order wave equation to a binary entropy gate defined by the Shannon entropy of a normalized identity field. When entropy remains within an admissible tolerance band, the system evolves freely; when the tolerance is exceeded, dissipation is triggered until admissibility is restored.

We prove that the resulting gated dynamics admit a Lyapunov functional whose dissipation is conditionally activated by entropy violation. This establishes global energy boundedness and guarantees recoverable identity preservation without continuous damping or hard constraints. The framework demonstrates that long-horizon stability can be achieved through invariant-triggered control rather than permanent suppression of dynamics.

The results provide a minimal, mathematically rigorous principle for adaptive stabilization applicable to physical fields, biological processes, and computational systems, and introduce entropy-triggered dissipation as a general control mechanism for identity-preserving evolution.