Application of Shannon Entropy to Reaction-Diffusion Problems Using the Stochastic Finite Difference Method

Area of Science:

• Physical Chemistry
• Statistical Mechanics
• Computational Science

Background:

• Diffusion processes are fundamental in various scientific disciplines.
• Characterizing diffusion dynamics often relies on traditional metrics that may not capture all aspects of particle distribution.
• A need exists for novel quantitative methods to assess diffusion behavior comprehensively.

Purpose of the Study:

• To introduce Shannon entropy as a metric for assessing concentration variability in diffusion processes.
• To demonstrate the utility of Shannon entropy in characterizing diffusion dynamics, mixing efficiency, and equilibrium states.
• To establish a computational framework for analyzing entropy evolution during diffusion.

Main Methods:

• Application of Shannon entropy to quantify spatial uncertainty in diffusing particle distributions.
• Numerical simulations employing the finite difference method.
• Utilization of the MAPLE 2025 symbolic computing environment for model implementation.
• Leveraging a previously validated computational framework for consistency.

Main Results:

• Shannon entropy effectively quantifies the uncertainty and disorder in particle distribution during diffusion.
• Entropy evolution demonstrates a clear correlation with diffusion kinetics and mixing processes.
• The computational model successfully illustrates the relationship between entropy changes and diffusion behavior.
• The findings validate Shannon entropy as a robust descriptor for diffusion-driven mixing.

Conclusions:

• Shannon entropy provides a novel and powerful metric for analyzing diffusion processes.
• This approach enhances the characterization of mixing efficiency and diffusion dynamics.
• Potential applications span engineering, environmental science, and biophysics, highlighting the broad relevance of this method.