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

## TL;DR

This paper explores how Shannon entropy can be used to study diffusion processes, offering new insights into mixing and particle distribution.

## Contribution

The paper introduces Shannon entropy as a novel metric for analyzing diffusion dynamics and mixing efficiency.

## Key findings

- Shannon entropy correlates with diffusion kinetics in numerical simulations.
- The method provides a robust way to describe diffusion-driven mixing.
- Applications span engineering, environmental science, and biophysics.

## Abstract

In this study, we introduce Shannon entropy as a key metric for assessing concentration variability in diffusion processes. Shannon entropy quantifies the uncertainty or disorder in the spatial distribution of diffusing particles, providing a novel perspective on diffusion dynamics. This proposed approach enables a more comprehensive characterization of mixing efficiency, equilibrium states, and transient diffusion behavior. Numerical simulations performed using the finite difference method in the MAPLE 2025 symbolic computing environment illustrate how entropy evolution correlates with diffusion kinetics. The computational model used in this study is based on a previously developed framework from our earlier research, ensuring consistency and validation of the results. The findings suggest that Shannon entropy can serve as a robust descriptor of diffusion-driven mixing, with potential applications in engineering, environmental science, and biophysics.