Novel mapping in non-equilibrium stochastic processes

James Heseltine, Eun Jin Kim

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

We investigate the time-evolution of a non-equilibrium system in view of the change in information and provide a novel mapping relation which quantifies the change in information far from equilibrium and the proximity of a non-equilibrium state to the attractor. Specifically, we utilize a nonlinear stochastic model where the stochastic noise plays the role of incoherent regulation of the dynamical variable x and analytically compute the rate of change in information (information velocity) from the time-dependent probability distribution function. From this, we quantify the total change in information in terms of information length L and the associated action J, where L represents the distance that the system travels in the fluctuation-based, statistical metric space parameterized by time. As the initial probability density function's mean position (μ) is decreased from the final equilibrium value (the carrying capacity), and increase monotonically with interesting power-law mapping relations. In comparison, as μ is increased from μ L and J increase slowly until they level off to a constant value. This manifests the proximity of the state to the attractor caused by a strong correlation for large μ through large fluctuations. Our proposed mapping relation provides a new way of understanding the progression of the complexity in non-equilibrium system in view of information change and the structure of underlying attractor.

Original languageEnglish
Article number175002
JournalJournal of Physics A: Mathematical and Theoretical
Volume49
Issue number17
DOIs
Publication statusPublished - 22 Mar 2016
Externally publishedYes

Fingerprint

stochastic processes
Random processes
Non-equilibrium
Stochastic Processes
Attractor
Stochastic models
Nonequilibrium Systems
Probability distributions
Probability density function
Distribution functions
Proximity
proximity
Quantify
Fluctuations
metric space
Carrying Capacity
probability distribution functions
Rate of change
Probability Distribution Function
probability density functions

Bibliographical note

This is an author-created, un-copyedited version of an article accepted for publication/published in Journal of Physics A: Mathematical and Theoretical. 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/10.1088/1751-8113/49/17/175002

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.

Keywords

  • Brownian motion
  • fluctuation phenomena
  • noise
  • non-equilibrium and irreversible thermodynamics
  • nonlinear dynamical systems
  • other topics in statistical physics
  • random processes
  • self-organized systems
  • thermodynamics

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)

Cite this

Novel mapping in non-equilibrium stochastic processes. / Heseltine, James; Kim, Eun Jin.

In: Journal of Physics A: Mathematical and Theoretical, Vol. 49, No. 17, 175002, 22.03.2016.

Research output: Contribution to journalArticle

@article{06c0036385e44ab2bf0c1af3633097f4,
title = "Novel mapping in non-equilibrium stochastic processes",
abstract = "We investigate the time-evolution of a non-equilibrium system in view of the change in information and provide a novel mapping relation which quantifies the change in information far from equilibrium and the proximity of a non-equilibrium state to the attractor. Specifically, we utilize a nonlinear stochastic model where the stochastic noise plays the role of incoherent regulation of the dynamical variable x and analytically compute the rate of change in information (information velocity) from the time-dependent probability distribution function. From this, we quantify the total change in information in terms of information length L and the associated action J, where L represents the distance that the system travels in the fluctuation-based, statistical metric space parameterized by time. As the initial probability density function's mean position (μ) is decreased from the final equilibrium value (the carrying capacity), and increase monotonically with interesting power-law mapping relations. In comparison, as μ is increased from μ∗ L and J increase slowly until they level off to a constant value. This manifests the proximity of the state to the attractor caused by a strong correlation for large μ through large fluctuations. Our proposed mapping relation provides a new way of understanding the progression of the complexity in non-equilibrium system in view of information change and the structure of underlying attractor.",
keywords = "Brownian motion, fluctuation phenomena, noise, non-equilibrium and irreversible thermodynamics, nonlinear dynamical systems, other topics in statistical physics, random processes, self-organized systems, thermodynamics",
author = "James Heseltine and Kim, {Eun Jin}",
note = "This is an author-created, un-copyedited version of an article accepted for publication/published in Journal of Physics A: Mathematical and Theoretical. 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/10.1088/1751-8113/49/17/175002 Copyright {\circledC} 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.",
year = "2016",
month = "3",
day = "22",
doi = "10.1088/1751-8113/49/17/175002",
language = "English",
volume = "49",
journal = "Journal of Physics A: Mathematical and Theoretical",
issn = "1751-8113",
publisher = "IOP Publishing",
number = "17",

}

TY - JOUR

T1 - Novel mapping in non-equilibrium stochastic processes

AU - Heseltine, James

AU - Kim, Eun Jin

N1 - This is an author-created, un-copyedited version of an article accepted for publication/published in Journal of Physics A: Mathematical and Theoretical. 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/10.1088/1751-8113/49/17/175002 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 - 2016/3/22

Y1 - 2016/3/22

N2 - We investigate the time-evolution of a non-equilibrium system in view of the change in information and provide a novel mapping relation which quantifies the change in information far from equilibrium and the proximity of a non-equilibrium state to the attractor. Specifically, we utilize a nonlinear stochastic model where the stochastic noise plays the role of incoherent regulation of the dynamical variable x and analytically compute the rate of change in information (information velocity) from the time-dependent probability distribution function. From this, we quantify the total change in information in terms of information length L and the associated action J, where L represents the distance that the system travels in the fluctuation-based, statistical metric space parameterized by time. As the initial probability density function's mean position (μ) is decreased from the final equilibrium value (the carrying capacity), and increase monotonically with interesting power-law mapping relations. In comparison, as μ is increased from μ∗ L and J increase slowly until they level off to a constant value. This manifests the proximity of the state to the attractor caused by a strong correlation for large μ through large fluctuations. Our proposed mapping relation provides a new way of understanding the progression of the complexity in non-equilibrium system in view of information change and the structure of underlying attractor.

AB - We investigate the time-evolution of a non-equilibrium system in view of the change in information and provide a novel mapping relation which quantifies the change in information far from equilibrium and the proximity of a non-equilibrium state to the attractor. Specifically, we utilize a nonlinear stochastic model where the stochastic noise plays the role of incoherent regulation of the dynamical variable x and analytically compute the rate of change in information (information velocity) from the time-dependent probability distribution function. From this, we quantify the total change in information in terms of information length L and the associated action J, where L represents the distance that the system travels in the fluctuation-based, statistical metric space parameterized by time. As the initial probability density function's mean position (μ) is decreased from the final equilibrium value (the carrying capacity), and increase monotonically with interesting power-law mapping relations. In comparison, as μ is increased from μ∗ L and J increase slowly until they level off to a constant value. This manifests the proximity of the state to the attractor caused by a strong correlation for large μ through large fluctuations. Our proposed mapping relation provides a new way of understanding the progression of the complexity in non-equilibrium system in view of information change and the structure of underlying attractor.

KW - Brownian motion

KW - fluctuation phenomena

KW - noise

KW - non-equilibrium and irreversible thermodynamics

KW - nonlinear dynamical systems

KW - other topics in statistical physics

KW - random processes

KW - self-organized systems

KW - thermodynamics

UR - http://www.scopus.com/inward/record.url?scp=84964054293&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/49/17/175002

DO - 10.1088/1751-8113/49/17/175002

M3 - Article

VL - 49

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 17

M1 - 175002

ER -