Site Number Dependence of Hysteresis in Binary Memory Models via Renormalization Group Approach Application to CO2 Reduction Reaction

This study extends the Binary Digit Memory (BDM) model and explores its application to CO_2 reduction catalysis. Originally developed to model memory induction through covalent modifications, the BDM model is a mathematical framework that describes switching dynamics in systems with multiple sites. We adapt this model for catalytic processes by coupling it with the Schrödinger equation to account for multi-electron dynamics on catalyst surfaces. The research is structured into three main chapters. Chapter 2: We perform a formal analysis of the BDM-ODE system using the mean-field approximation. This approach simplifies the high-dimensional system and reveals critical phenomena such as hysteresis and bifurcations, which are essential for understanding catalytic behavior. Chapter 3: We refine these findings using renormalization group (RG) theory, which rigorously justifies the mean-field approximation and uncovers the scaling universality of the system's critical behavior as the number of sites, N , increases. This universality ensures consistency in predictions across different scales. Chapter 4: We apply this framework to CO₂ reduction. We introduce a coupled system where the Schrödinger equation governs electron dynamics on the catalyst surface, while the BDM-ODE system manages the switching dynamics. Using the Hartree approximation and RG-validated mean-field methods, we simulate the CO₂ reduction process and optimize catalytic performance. Simulations demonstrate significant improvements in yield and efficiency. This interdisciplinary approach integrates nonlinear dynamics and quantum mechanics, offering new insights into CO₂ reduction catalysis. By leveraging the strengths of the BDM model and combining it with quantum mechanical principles, we establish a robust theoretical foundation for enhancing catalytic processes, with potential implications for sustainable energy solutions.