Wakayama University · Faculty of Systems Engineering

Research keywordsgeneralized Langevin equation・fluctuating diffusivity・anomalous diffusion・ergodicity breaking・slow relaxation・Brownian yet non-Gaussian diffusion・elastic networks・statistical physics

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• Anomalous statistics in the Langevin equation with fluctuating diffusivity: from Brownian yet non-Gaussian diffusion to anomalous diffusion and ergodicity breaking2026 · Abstract Diffusive motion is a fundamental transport mechanism in physical and biological systems, governing dynamics across a wide range of scales---from molecular transport to animal foraging. In many complex systems, however, diffusion deviates from classical Brownian behaviour, exhibiting striking phenomena such as Brownian yet non-Gaussian diffusion (BYNGD) and anomalous diffusion.
BYNGD describes a frequently observed statistical feature characterised by the coexistence of linear mean-square displacement (MSD) and non-Gaussian displacement distributions. Anomalous diffusion, in contrast, involves a nonlinear time dependence of the MSD and often reflects mechanisms such as trapping, viscoelasticity, heterogeneity, or active processes. Both phenomena challenge the conventional framework based on constant diffusivity and Gaussian statistics. This review focuses the theoretical modelling of such behaviour via the Langevin equation with fluctuating diffusivity (LEFD)---a flexible stochastic framework that captures essential features of diffusion in heterogeneous media. LEFD not only accounts for BYNGD but also naturally encompasses a wide range of anomalous transport phenomena, including subdiffusion, ageing, and weak ergodicity breaking. Ergodicity is discussed in terms of the correspondence between time and ensemble averages, as well as the trajectory-to-trajectory variability of time-averaged observables. The review further highlights the empirical relevance of LEFD and related models in explaining diverse experimental observations and underscores their value to uncovering the physical mechanisms governing transport in complex systems.
• Memory-induced slow relaxation in the generalized Langevin equation2025 · Makoto Shimizu, Tomoshige Miyaguchi, Eiji Yamamoto, Takuma Akimoto
• Generalized Langevin dynamics for single beads in linear elastic networks2024 · Soya Shinkai, Shuichi Onami, Tomoshige Miyaguchi
• Generalized Langevin equation with fluctuating diffusivity2022 · Tomoshige Miyaguchi

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