This study introduces and reexamines a novel evaluation method that integrates Malliavin derivatives with fractal properties to predict plasma fluctuations within a collisional-radiative model framework using transfer entropy. This approach is applied to nanoparticle technologies across various industrial sectors and forensic science. The influence of interactions with metastable atoms on the overall system is investigated in glow discharge plasma. The effects of gas temperature, pressure, electron temperature, and density on system behavior are evaluated. Furthermore, the system's tendency to reach a steady state is verified to be significantly influenced by the atomic state. This method is expected to improve the understanding of plasma physics and accelerate chemical analysis and semiconductor miniaturization.
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