Markov Blanket Density and Free Energy Minimization

This paper presents a continuous, information-theoretic extension of the Free Energy Principle through the concept of Markov blanket density—a scalar field that quantifies the degree of conditional independence between internal and external states at each point in space (ranging from 0 for full coupling to 1 for full separation). It demonstrates that active inference dynamics—including the minimization of variational and expected free energy—naturally emerge from spatial gradients in this density, making Markov blanket density a necessary foundation for the definability and coherence of the Free Energy Principle. These ideas are developed through a mathematically framework that links density gradients to precise and testable dynamics, offering a foundation for novel predictions and simulation paradigms.