Paper VIII - From Statistical Rarity to Dynamical Stability: A Constraint-Based Framework for Functional Information

This paper is part of the Infropy / Constraint Dynamics Series (Paper VIII of VIII) and develops a dynamical framework for understanding functional information in nonequilibrium systems. While functional information is often defined in terms of the statistical rarity of configurations capable of achieving a specified outcome, such formulations do not fully specify the physical processes by which these configurations are constructed and stabilized. The paper proposes that functional information arises from constraint-mediated stabilization, in which interactions among system components generate constraints that restrict accessible degrees of freedom, channel energy flow, and stabilize specific configurations over time. As these constraints accumulate and interact, they increase the persistence and reproducibility of certain system states. Within this framework, persistence time provides a quantitative bridge between dynamical stability and functional description, linking functional information to measurable quantities such as transition rates and escape dynamics. Extending the framework across levels of system description, the paper introduces cross-scale constraint coupling, in which higher-level structures stabilize lower-level dynamics while lower-level interactions contribute to higher-level structure. This formulation reframes functional information as a dynamical consequence of constraint formation and persistence, providing a pathway for integrating statistical and physical descriptions of functional structure within a unified framework. It builds on the preceding papers and remains consistent with nonequilibrium thermodynamics without introducing new physical laws. Version 1.2: Formatting and references standardized for consistency across the Infropy / Constraint Dynamics Series. No substantive changes to content have been made.