Correlation between the first-reaction time and the acquired boundary local time.

Area of Science:

• Statistical Physics
• Chemical Physics
• Physical Chemistry

Background:

• Particle diffusion is fundamental in many physical and chemical processes.
• Understanding particle-boundary interactions is crucial for reaction dynamics.
• First-reaction time and boundary local time are key metrics in diffusion studies.

Purpose of the Study:

• To investigate the statistical correlation between a diffusing particle's first-reaction time and its accumulated boundary local time.
• To develop a universal theoretical framework for deriving the joint probability density and correlation coefficient.
• To analyze the influence of boundary reactivity, shape, and interior obstacles on these correlations.

Main Methods:

• Development of a universal theoretical framework.
• Derivation of analytical solutions for basic domains.
• Complementary Monte Carlo simulations for disordered media and interior obstacles.

Main Results:

• Established an intrinsic link between first-reaction time and boundary local time.
• Derived the joint probability density and correlation coefficient.
• Demonstrated dependence of correlations on boundary properties and presence of obstacles.

Conclusions:

• The developed framework provides a universal approach to understand diffusion-reaction dynamics.
• Analytical and simulation results offer insights into systems with varying complexity.
• The findings have potential applications in chemical physics and materials science.