Computational Modeling and Analytical Assessment of Uncertainty Behavior in Complex Entropic Systems

Abstract

Uncertainty quantification in entropic systems has emerged as a critical domain within computational physics, statistical mechanics, and complex systems modeling, where nonlinear interactions and stochastic variability significantly affect predictive reliability. This study presents a computational and analytical framework for modeling uncertainty behavior in complex entropic systems using a hybrid approach combining stochastic modeling principles, sensitivity analysis, and probabilistic inference techniques. The research builds upon established methodologies in emission uncertainty modeling and time-series-based probabilistic systems analysis (Abdel-Aziz & Frey, 2003), extending them into generalized entropic domains.
The proposed framework integrates structured uncertainty decomposition, entropy-based state representation, and variance propagation modeling to capture both intrinsic system randomness and external perturbation effects. Empirical alignment is conceptually supported using previously validated uncertainty quantification strategies from environmental emission systems (Frey, 2003; Frey & Bammi, 2002). The study further evaluates how uncertainty evolves under nonlinear entropic transformations and examines the sensitivity of system outputs to stochastic parameter fluctuations.
Results indicate that uncertainty in entropic systems is highly path-dependent, non-Gaussian in distribution, and significantly influenced by underlying structural entropy gradients. The findings highlight the necessity of hybrid analytical-computational frameworks for robust modeling of high-dimensional stochastic systems. The study contributes to improved theoretical understanding and practical modeling of uncertainty propagation in complex systems with applications in physics, engineering, and data-driven simulation environments.