A Variational Feedback–Entropy Framework for Multi-Scale Structure Formation: From Gravitational Systems to Neural Inference Dynamics

Abstract We present a variational formulation of structure formation and adaptive dynamics in physical, biological, and cognitive systems. System evolution is modeled as gradient flow on a free-energy functional subject to a thermodynamic entropy-production constraint. We demonstrate formal equivalence between this variational principle, nonlinear feedback dynamical systems, and established frameworks including Friston's free-energy principle and Jeans gravitational instability. The framework functions as a unifying meta-theoretical description and does not replace the underlying domain-specific theories. Stability conditions, phase transitions, and testable predictions are derived from the geometry of the free-energy landscape.