Distributional behavior of diffusion coefficients obtained by single trajectories in annealed transit time model. (1st December 2016)

• Record Type: Journal Article
• Authors: Akimoto, Takuma; Yamamoto, Eiji
• Is Part Of: Journal of statistical mechanics. (2016:Dec.)
• Publication Date: 2016-12-01
• Subjects: 4 -- 11; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/2016/12/123201
• Languages: English
• ISSNs: 1742-5468

Abstract

Abstract: Local diffusion coefficients in disordered systems such as spin glass systems and living cells are highly heterogeneous and may change over time. Such a time-dependent and spatially heterogeneous environment results in irreproducibility of single-particle-tracking measurements. Irreproducibility of time-averaged observables has been theoretically studied in the context of weak ergodicity breaking in stochastic processes. Here, we provide rigorous descriptions of equilibrium and non-equilibrium diffusion processes for the annealed transit time model, which is a heterogeneous diffusion model in living cells. We give analytical solutions for the mean square displacement (MSD) and the relative standard deviation of the time-averaged MSD for equilibrium and non-equilibrium situations. We find that the time-averaged MSD grows linearly with time and that the time-averaged diffusion coefficients are intrinsically random (irreproducible) even in the long-time measurements in non-equilibrium situations. Furthermore, the distribution of the time-averaged diffusion coefficients converges to a universal distribution in the sense that it does not depend on initial conditions. Our findings pave the way for a theoretical understanding of distributional behavior of the time-averaged diffusion coefficients in disordered systems.