Conjugate Information-Energy Entropy Modeling and Entropy Gradient Control Analysis Based on Cyber-Physical Integration

The core challenge of cyber-physical integration technology in Energy Internet lies in effectively fusing multi-energy heterogeneous data across physical and information layers. To address this issue, this study proposes a novel information-energy synergistic control theory based on energy cascade utilization. The key innovation resides in constructing the conjugate information-energy entropy model, which integrates thermodynamic entropy and information entropy to define a conjugate entropy function for quantifying systemic chaos. Building upon this, the negative entropy-driven optimization framework is established, leveraging information flow to proactively offset energy entropy increase, thereby forming a synergistic optimization mechanism where information empowers energy. The convergence of the entropy gradient-driven algorithm is rigorously proven using Lyapunov stability theory. Simulation results demonstrate that the proposed model exhibits robust support for the co-evolution of heterogeneous energy flows. When subjected to fault disturbances, the system demonstrates strong self-healing capability while sustaining entropy reduction to ensure systematic order. Empirical validation in a regional integrated energy system demonstrates that the proposed model enhances renewable energy accommodation capacity significantly, providing a novel theoretical tool and methodological foundation for dynamic optimization and mechanism analysis of Energy Internet.