Constraint Dynamics of Coherence: A Relaxation-Based Framework for Living Systems

This paper develops a unified theoretical framework for understanding how organized systems persist across scales. The starting point is the observation that all physical systems exhibit relaxation—the passive decay of gradients over time. Persistence therefore requires counteracting relaxation through constraint architecture and active maintenance.

The framework is built layer by layer:

• Gradients (pressure, temperature, concentration, potential) as the substrate of dynamics

• Flow as the expression of gradients

• Boundaries and constraints as modulators of relaxation rates

• Structure as stabilized constraint (geometry, networks, loops)

• Proto-coherence: passive persistence through structure alone

• Active coherence: maintenance regimes where restoration (τ_m) outpaces relaxation (τ_r)

• Scaling: coherence radius and size limits

• Failure: rate imbalance, collapse modes, hysteresis

• Interaction: coupling between coherent systems

• Observer emergence: internal state variables and informational regulation

The framework yields operational definitions, a variable atlas for measurement, and testable conditions. It is intended to provide a common language for analyzing persistence in physical, biological, and social systems.