Information-Energy Density Conservation and Transformation Law: A New Physical Law for Cosmic Evolution and Golden Spiral Optimal Path in DCD Framework

Based on our previously established Diffusion-Cohesion Dynamics (DCD) theoretical framework [1–7], this paper discovers and formalizes a new physical law: the Information-Energy Density Conservation and Transformation Law. This law states that for any self-organizing complex system, the product of information density (I) and energy processing efficiency (E) follows an exponential growth pattern, with the optimal growth path being the golden spiral. Through rigorous derivation from the DCD equations, we prove that when a system evolves under critical coupling conditions (δ ≈ δmin), the I×E product grows exponentially at a constant rate, and each reorganization event leads to an efficiency improvement by the golden ratio ϕ ≈ 1.618. This law unifies multi-scale phenomena from quantum computing to cosmic evolution and provides precise design specifications for next-generation adaptive computing chips.