Quaternionic–Fractional Kinetic Operator: An Entropy-Based Framework for Competitive and Uncertain Chemical Reactions

This work proposes a quaternionic–fractional kinetic operator to generalize classical chemical kinetics by embedding entropy-driven corrections. In this framework, reaction pathways are represented as quaternionic weights, where the scalar component encodes global reactivity and the vector component introduces anisotropic interactions. An angular error operator is incorporated as an entropy-like metric of uncertainty, quantifying deviations between theoretical and experimental orientations. Additionally, fractional chemical potentials are introduced to account for memory effects, extending kinetics beyond the Markovian regime. Synthetic simulations demonstrate that the operator recovers classical laws as limiting cases, while predicting non-exponential and anisotropic trends when uncertainty, interference, and entropic memory dominate. Figures 1–12 illustrate the roles of quaternionic corrections, angular misalignment, and fractional persistence in shaping the kinetic response. The approach provides a unified interpretation of uncertainty, anisotropy, and memory within chemical kinetics, offering potential applications in heterogeneous catalysis, biochemical networks, and energy materials where classical exponential kinetics fail. While this study is based on numerical modeling, the results lay the groundwork for future experimental validation and integration with data-driven approaches.