Conveners
Lecture 6: Introduction to Stochastic Theories for Anomalous Diffusion Processes in Living Systems (Prof. Jae-Hyung Jeon)
- Tetsuya Hiraiwa (Institute of Physics, Academia Sinica)
Description
Anomalous diffusion, referring to deviations from classical Brownian motion, is often observed in living cells where macromolecules move in crowded, heterogeneous, and often actively driven environments. This talk offers a pedagogical introduction to the physics of anomalous diffusion in biological systems, starting from the historical foundations of Brownian motion and Einstein–Langevin theory and progressing to modern experimental observations from single-particle tracking and super-resolution microscopy. We will discuss how intracellular transport exhibits subdiffusion, superdiffusion, non-Gaussian displacement statistics, and trajectory-to-trajectory variability, signaling the breakdown of classical diffusion paradigms. To explain these phenomena, several stochastic models will be introduced, including continuous-time random walks, fractional Brownian motion and fractional Langevin equations, diffusion on fractal or obstructed media, Lévy walks, and random diffusivity models. Emphasis will be placed on key physical concepts, such as the roles of memory, heterogeneity, and activity, the distinction between time- versus ensemble-averaged observables, and ergodicity breaking.
