### Abstract

We investigate information geometry in a toy model of self-organised shear flows, where a bimodal PDF of x with two peaks signifying the formation of mean shear gradients is induced by a finite memory time of a stochastic forcing f. We calculate time-dependent probability density functions (PDFs) for different values of the correlation time and amplitude D of the stochastic forcing, and identify the parameter space for unimodal and bimodal stationary PDFs. By comparing results with those obtained under the uniform coloured noise approximation (UCNA) in Jacquet et al (2018 Entropy 20 613), we find that UCNA tends to favor the formation of a bimodal PDF of x for given parameter values and D. We map out attractor structure associated with unimodal and bimodal PDFs of x by measuring the total information length against the location x
_{0}
of a narrow initial PDF of x. Here represents the total number of statistically different states that a system passes through in time. We examine the validity of the UCNA from the perspective of information change and show how to fine-tune an initial joint PDF of x and f to achieve a better agreement with UCNA results.

Original language | English |
---|---|

Article number | 023204 |

Journal | Journal of Statistical Mechanics: Theory and Experiment |

Volume | 2019 |

Issue number | 2 |

DOIs | |

Publication status | Published - 20 Feb 2019 |

Externally published | Yes |

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### Bibliographical note

This is an author-created, un-copyedited version of an article accepted for publication/published in Journal of Statistical Mechanics: Theory and Experiment IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://dx.doi.org/10.1088/1742-5468/ab00ddCopyright © and Moral Rights are retained by the author(s) and/ or other copyright owners. A copy can be downloaded for personal non-commercial research or study, without prior permission or charge. This item cannot be reproduced or quoted extensively from without first obtaining permission in writing from the copyright holder(s). The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the copyright holders.

### Keywords

- fluctuation phenomena
- stochastic processes

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Statistics, Probability and Uncertainty

### Cite this

*Journal of Statistical Mechanics: Theory and Experiment*,

*2019*(2), [023204]. https://doi.org/10.1088/1742-5468/ab00dd

**Information geometry in a reduced model of self-organised shear flows without the uniform coloured noise approximation.** / Kim, Eun Jin; Jacquet, Quentin; Hollerbach, Rainer.

Research output: Contribution to journal › Article

*Journal of Statistical Mechanics: Theory and Experiment*, vol. 2019, no. 2, 023204. https://doi.org/10.1088/1742-5468/ab00dd

}

TY - JOUR

T1 - Information geometry in a reduced model of self-organised shear flows without the uniform coloured noise approximation

AU - Kim, Eun Jin

AU - Jacquet, Quentin

AU - Hollerbach, Rainer

N1 - This is an author-created, un-copyedited version of an article accepted for publication/published in Journal of Statistical Mechanics: Theory and Experiment IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://dx.doi.org/10.1088/1742-5468/ab00dd Copyright © and Moral Rights are retained by the author(s) and/ or other copyright owners. A copy can be downloaded for personal non-commercial research or study, without prior permission or charge. This item cannot be reproduced or quoted extensively from without first obtaining permission in writing from the copyright holder(s). The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the copyright holders.

PY - 2019/2/20

Y1 - 2019/2/20

N2 - We investigate information geometry in a toy model of self-organised shear flows, where a bimodal PDF of x with two peaks signifying the formation of mean shear gradients is induced by a finite memory time of a stochastic forcing f. We calculate time-dependent probability density functions (PDFs) for different values of the correlation time and amplitude D of the stochastic forcing, and identify the parameter space for unimodal and bimodal stationary PDFs. By comparing results with those obtained under the uniform coloured noise approximation (UCNA) in Jacquet et al (2018 Entropy 20 613), we find that UCNA tends to favor the formation of a bimodal PDF of x for given parameter values and D. We map out attractor structure associated with unimodal and bimodal PDFs of x by measuring the total information length against the location x 0 of a narrow initial PDF of x. Here represents the total number of statistically different states that a system passes through in time. We examine the validity of the UCNA from the perspective of information change and show how to fine-tune an initial joint PDF of x and f to achieve a better agreement with UCNA results.

AB - We investigate information geometry in a toy model of self-organised shear flows, where a bimodal PDF of x with two peaks signifying the formation of mean shear gradients is induced by a finite memory time of a stochastic forcing f. We calculate time-dependent probability density functions (PDFs) for different values of the correlation time and amplitude D of the stochastic forcing, and identify the parameter space for unimodal and bimodal stationary PDFs. By comparing results with those obtained under the uniform coloured noise approximation (UCNA) in Jacquet et al (2018 Entropy 20 613), we find that UCNA tends to favor the formation of a bimodal PDF of x for given parameter values and D. We map out attractor structure associated with unimodal and bimodal PDFs of x by measuring the total information length against the location x 0 of a narrow initial PDF of x. Here represents the total number of statistically different states that a system passes through in time. We examine the validity of the UCNA from the perspective of information change and show how to fine-tune an initial joint PDF of x and f to achieve a better agreement with UCNA results.

KW - fluctuation phenomena

KW - stochastic processes

UR - http://www.scopus.com/inward/record.url?scp=85062485027&partnerID=8YFLogxK

U2 - 10.1088/1742-5468/ab00dd

DO - 10.1088/1742-5468/ab00dd

M3 - Article

VL - 2019

JO - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

SN - 1742-5468

IS - 2

M1 - 023204

ER -