Deep Personal Privacy as Network Impedance: A Diffusion-Based Model of Knowledge Flow

Abstract

This paper introduces a novel theoretical and mathematical framework for Deep Personal Privacy (DPP), conceptualized as a network-level impedance to the diffusion of knowledge about individuals. Moving beyond traditional binary notions of privacy as secrecy versus disclosure, the model reframes privacy as a dynamic, system-wide resistance governing the propagation of novel information across interconnected data ecosystems. By integrating graph-theoretic structures with a novelty-driven, nonconservative diffusion process, the framework captures the non-rival and accumulative nature of knowledge. A central innovation is the identification of the directed novelty gradient as the unifying driver of both knowledge diffusion and privacy erosion. The analysis further shows that AI systems act as high-connectivity inference hubs that structurally reduce privacy impedance and accelerate adversarial knowledge acquisition. The proposed DPP framework establishes a rigorous link between network topology, diffusion dynamics, and privacy loss, positioning privacy as a measurable, system-level property and offering a new foundation for ethical and regulatory analysis in AI-driven environments.