Deviation of the statistical fluctuation in heterogeneous anomalous diffusion

TL;DR

This paper investigates the statistical fluctuations of anomalous diffusion exponents in heterogeneous cellular environments, proposing a Gaussian deviation model based on thermodynamic fluctuation theory to better understand their statistical properties.

Contribution

It introduces a Gaussian deviation framework for the fluctuation distribution of anomalous diffusion exponents, extending previous maximum-entropy approaches with thermodynamic fluctuation analysis.

Findings

Deviation follows a multivariate Gaussian distribution

The approach links fluctuation deviations to thermodynamic principles

Provides a theoretical basis for understanding heterogeneity in diffusion

Abstract

The exponent of anomalous diffusion of virus in cytoplasm of a living cell is experimentally known to fluctuate depending on localized areas of the cytoplasm, indicating heterogeneity of diffusion. In a recent paper (Itto, 2012), a maximum-entropy-principle approach has been developed in order to propose an Ansatz for the statistical distribution of such exponent fluctuations. Based on this approach, here the deviation of the statistical distribution of the fluctuations from the proposed one is studied from the viewpoint of Einstein's theory of fluctuations (of the thermodynamic quantities). This may present a step toward understanding the statistical property of the deviation. It is shown in a certain class of small deviations that the deviation obeys the multivariate Gaussian distribution.