### Abstract

We consider the Langevin equation with dichotomously fluctuating diffusivity, where the diffusion coefficient changes dichotomously over time, in order to study fluctuations of time-averaged observables in temporally heterogeneous diffusion processes. We find that the time-averaged mean-square displacement (TMSD) can be represented by the occupation time of a state in the asymptotic limit of the measurement time and hence occupation time statistics is a powerful tool for calculating the TMSD in the model. We show that the TMSD increases linearly with time (normal diffusion) but the time-averaged diffusion coefficients are intrinsically random when the mean sojourn time for one of the states diverges, i.e., intrinsic nonequilibrium processes. Thus, we find that temporally heterogeneous environments provide anomalous fluctuations of time-averaged diffusivity, which have relevance to large fluctuations of the diffusion coefficients obtained by single-particle-tracking trajectories in experiments.

Original language | English |
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Article number | 062109 |

Journal | Physical Review E |

Volume | 93 |

Issue number | 6 |

DOIs | |

Publication status | Published - 2016 Jun 6 |

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### ASJC Scopus subject areas

- Statistics and Probability
- Condensed Matter Physics
- Statistical and Nonlinear Physics

### Cite this

**Distributional behaviors of time-averaged observables in the Langevin equation with fluctuating diffusivity : Normal diffusion but anomalous fluctuations.** / Akimoto, Takuma; Yamamoto, Eiji.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Distributional behaviors of time-averaged observables in the Langevin equation with fluctuating diffusivity

T2 - Normal diffusion but anomalous fluctuations

AU - Akimoto, Takuma

AU - Yamamoto, Eiji

PY - 2016/6/6

Y1 - 2016/6/6

N2 - We consider the Langevin equation with dichotomously fluctuating diffusivity, where the diffusion coefficient changes dichotomously over time, in order to study fluctuations of time-averaged observables in temporally heterogeneous diffusion processes. We find that the time-averaged mean-square displacement (TMSD) can be represented by the occupation time of a state in the asymptotic limit of the measurement time and hence occupation time statistics is a powerful tool for calculating the TMSD in the model. We show that the TMSD increases linearly with time (normal diffusion) but the time-averaged diffusion coefficients are intrinsically random when the mean sojourn time for one of the states diverges, i.e., intrinsic nonequilibrium processes. Thus, we find that temporally heterogeneous environments provide anomalous fluctuations of time-averaged diffusivity, which have relevance to large fluctuations of the diffusion coefficients obtained by single-particle-tracking trajectories in experiments.

AB - We consider the Langevin equation with dichotomously fluctuating diffusivity, where the diffusion coefficient changes dichotomously over time, in order to study fluctuations of time-averaged observables in temporally heterogeneous diffusion processes. We find that the time-averaged mean-square displacement (TMSD) can be represented by the occupation time of a state in the asymptotic limit of the measurement time and hence occupation time statistics is a powerful tool for calculating the TMSD in the model. We show that the TMSD increases linearly with time (normal diffusion) but the time-averaged diffusion coefficients are intrinsically random when the mean sojourn time for one of the states diverges, i.e., intrinsic nonequilibrium processes. Thus, we find that temporally heterogeneous environments provide anomalous fluctuations of time-averaged diffusivity, which have relevance to large fluctuations of the diffusion coefficients obtained by single-particle-tracking trajectories in experiments.

UR - http://www.scopus.com/inward/record.url?scp=85004098372&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85004098372&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.93.062109

DO - 10.1103/PhysRevE.93.062109

M3 - Article

VL - 93

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 1063-651X

IS - 6

M1 - 062109

ER -