Fractional kinetics emerging from ergodicity breaking in random media

Area of Science:

• Physics
• Biophysics
• Statistical Mechanics

Background:

• Diffusion in biological systems often deviates from simple Brownian motion.
• Complex cellular environments exhibit heterogeneity and dynamic processes affecting particle movement.

Purpose of the Study:

• To present a novel modeling approach for diffusion in complex media with random length scales.
• To explain subdiffusion phenomena observed in living cells, including ergodicity breaking.

Main Methods:

• Developed a stochastic process model incorporating a random length scale.
• Analyzed the model's behavior in relation to single-particle tracking experiments.
• Investigated the connection between ergodicity breaking and fractional diffusion kinetics.

Main Results:

• The model exhibits subdiffusion consistent with experimental observations like ergodicity breaking, p variation, and aging.
• The approach unifies features of fractional Brownian motion and continuous-time random walks.
• A single parameter governs the ergodic-to-nonergodic transition and the shift from nonfractional to fractional diffusion.

Conclusions:

• Fractional diffusion kinetics naturally emerge from ergodicity breaking in complex media.
• The proposed model provides a unified framework for understanding anomalous diffusion in biological systems.