# Fractional kinetics emerging from ergodicity breaking in random media

Source: [Fractional kinetics emerging from ergodicity breaking in random media](<https://www.sota2.com/research/paper/68fa34e61e209131ce89d0c7>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T20:56:56.883Z

Authors: Daniel Molina-Garc\\'ia, Tuan Minh Pham, Paolo Paradisi, Carlo Manzo, Gianni Pagnini

Published: 2015-08-06T11:03:19.000Z

## Abstract

We present a modelling approach for diffusion in a complex medium characterized by a random length scale. The resulting stochastic process shows subdiffusion with a behavior in qualitative agreement with single particle tracking experiments in living cells, such as ergodicity breaking, p-variation and aging. In particular, this approach recapitulates characteristic features previously described in part by the fractional Brownian motion and in part by the continuous-time random walk. Moreover, for a proper distribution of the length scale, a single parameter controls the ergodic-to-nonergodic transition and, remarkably, also drives the transition of the diffusion equation of the process from non-fractional to fractional, thus demonstrating that fractional kinetics emerges from ergodicity breaking.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1508.01361>)

[PDF](<https://arxiv.org/pdf/1508.01361.pdf>)