Resolving Nanoscale Reaction Kinetics: A Unified Framework from Classical Chemistry to Quantum Collectivity - Barack Ndenga (Publisher, 2025)
At the nanoscale, the classical separation between molecular reactivity and quantum collective behavior collapses. Conventional chemical kinetics—grounded in transition-state theory, Arrhenius scaling, and continuum thermodynamics—fails to describe reactions occurring in domains where particle numbers are small, energy landscapes are strongly quantized, and coherence competes with dissipation. In this work, I propose a unified theoretical framework that seamlessly bridges classical kinetics with emergent quantum collectivity in nanosystems. My approach integrates: discrete-state stochastic kinetics, quantum master equations, collective vibrational/photonic coupling, topological constraints, and non-extensive thermodynamic corrections unique to nanoscale systems. I demonstrate how nanoscale reaction rates deviate systematically from classical predictions and how quantum correlations, confinement, and collective coherent modes reshape both reaction pathways and energy transfer. This framework resolves long-standing inconsistencies observed in nanocatalysis, reaction dynamics in quantum dots, plasmonic hot-electron chemistry, and molecular clusters. I conclude that nanoscale chemistry is neither “classical” nor “molecular quantum” but an intermediate regime governed by quantized collectivity, requiring a new kinetic law that I derive in closed form.
This article presents a complete theoretical resolution of nanoscale reaction kinetics, where classical chemical mechanisms collapse and quantum collective effects dominate. I introduce the Unified Nano-Kinetic Law (UNKL), a new formulation that incorporates quantized energy barriers, coherence-modified transition rates, collective vibrational and plasmonic modes, and topologically constrained reaction pathways. Using a combination of quantum master equations, stochastic path-integral sampling, and non-extensive statistical mechanics, I demonstrate how nanoscale systems transition from classical to quantum-collective behavior. This work resolves long-standing inconsistencies in nanocatalysis, hot-electron chemistry, and cluster reactivity, offering the first general kinetic law valid from molecular to nanoscale quantum-regime systems.