“MWK” model and the quantum inertia of confined nanosystems

This paper introduces the “MWK” model to characterize the physics of nanosystems through the lens of quantum inertia. The framework establishes a fundamental proportional relationship between mass change in a nanosystem and its surface chemical rate constant, defining a novel K-rate with k-wave equivalence. This approach bridges traditional chemical kinetics, governed by the reaction constant (K), with quantum scattering theory, where the wave vector (k) dictates particle momentum and collision mechanics. By unifying thermodynamic, relativistic, and quantum considerations via Fermi-type calculations, the model derives new parameters to define nanoscale inertial states in bio-nanomaterials. Integrating Einstein-Planck-De Broglie principles reveals a working quantum-relativistic connection under the momentum form, which governs the system scale factor. This scale represents a hybrid action-length nano-inertia. It directly encodes both the effective mass of the primary energy carrier (e.g., electron, exciton, proton, or quasiparticle) and the characteristic coherence length scale, such as MOF pore size or tunneling distance. These findings provide a qualified theoretical foundation for quantum inertia in nanostructures, advancing predictive modeling and stimulating further topo-quantum research into advanced nanotechnology applications.