# Ergodic and Nonergodic Anomalous Diffusion in Coupled Stochastic Processes

Source: [Ergodic and Nonergodic Anomalous Diffusion in Coupled Stochastic Processes](<https://www.sota2.com/research/paper/68fa23b52c2a37601939b259>)

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

Data updated: 2025-10-28T13:52:37.925Z

Authors: Golan Bel, Ilya Nemenman

Published: 2009-01-29T21:35:05.000Z

## Abstract

Inspired by problems in biochemical kinetics, we study statistical properties of an overdamped Langevin process whose friction coefficient depends on the state of a similar, unobserved process. Integrating out the latter, we derive the long time behaviour of the mean square displacement. Anomalous diffusion is found. Since the diffusion exponent can not be predicted using a simple scaling argument, anomalous scaling appears as well. We also find that the coupling can lead to ergodic or non-ergodic behaviour of the studied process. We compare our theoretical predictions with numerical simulations and find an excellent agreement. The findings caution against treating biochemical systems coupled with unobserved dynamical degrees of freedom by means of standard, diffusive Langevin descriptions.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/0901.4785>)

[PDF](<https://arxiv.org/pdf/0901.4785.pdf>)