Investigation of the statistical distance to reach stationary distributions

S. B. Nicholson; Eun Jin Kim

doi:10.1016/j.physleta.2014.11.003

Investigation of the statistical distance to reach stationary distributions

S. B. Nicholson, Eun Jin Kim

University of Sheffield

Research output: Contribution to journal › Article › peer-review

29 Citations (Scopus)

43 Downloads (Pure)

Abstract

The thermodynamic length gives a Riemannian metric to a system's phase space. Here we extend the traditional thermodynamic length to the information length (L) out of equilibrium and examine its properties. We utilise L as a useful methodology of analysing non-equilibrium systems without evoking conventional assumptions such as Gaussian statistics, detailed balance, priori-known constraints, or ergodicity and numerically examine how L evolves in time for the logistic map in the chaotic regime depending on initial conditions. To this end, we propose a discrete version of L which is mathematically well defined by taking a set theoretic approach. We identify the areas of phase space where the loss of information of the system takes place most rapidly. In particular, we present an interesting result that the unstable fixed points turn out to most efficiently drive the logistic map towards a stationary distribution through L.

Original language	English
Pages (from-to)	83-88
Number of pages	6
Journal	Physics Letters A
Volume	379
Issue number	3
Early online date	7 Nov 2014
DOIs	https://doi.org/10.1016/j.physleta.2014.11.003
Publication status	Published - 23 Jan 2015
Externally published	Yes

Bibliographical note

NOTICE: this is the author’s version of a work that was accepted for publication in Physics Letters A. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Physics Letters A, Vol. 379, (2014) DOI: 10.1016/j.physleta.2014.11.003

© 2014, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/

Keywords

Logistic map
Non-equilibrium
Relaxation
Thermodynamic length

ASJC Scopus subject areas

Physics and Astronomy(all)

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10.1016/j.physleta.2014.11.003

Post-PrintAccepted author manuscript, 912 KBLicence: CC BY-NC-ND

Cite this

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title = "Investigation of the statistical distance to reach stationary distributions",

abstract = "The thermodynamic length gives a Riemannian metric to a system's phase space. Here we extend the traditional thermodynamic length to the information length (L) out of equilibrium and examine its properties. We utilise L as a useful methodology of analysing non-equilibrium systems without evoking conventional assumptions such as Gaussian statistics, detailed balance, priori-known constraints, or ergodicity and numerically examine how L evolves in time for the logistic map in the chaotic regime depending on initial conditions. To this end, we propose a discrete version of L which is mathematically well defined by taking a set theoretic approach. We identify the areas of phase space where the loss of information of the system takes place most rapidly. In particular, we present an interesting result that the unstable fixed points turn out to most efficiently drive the logistic map towards a stationary distribution through L.",

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note = "NOTICE: this is the author{\textquoteright}s version of a work that was accepted for publication in Physics Letters A. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Physics Letters A, Vol. 379, (2014) DOI: 10.1016/j.physleta.2014.11.003 {\textcopyright} 2014, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/ ",

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AU - Nicholson, S. B.

AU - Kim, Eun Jin

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PY - 2015/1/23

Y1 - 2015/1/23

N2 - The thermodynamic length gives a Riemannian metric to a system's phase space. Here we extend the traditional thermodynamic length to the information length (L) out of equilibrium and examine its properties. We utilise L as a useful methodology of analysing non-equilibrium systems without evoking conventional assumptions such as Gaussian statistics, detailed balance, priori-known constraints, or ergodicity and numerically examine how L evolves in time for the logistic map in the chaotic regime depending on initial conditions. To this end, we propose a discrete version of L which is mathematically well defined by taking a set theoretic approach. We identify the areas of phase space where the loss of information of the system takes place most rapidly. In particular, we present an interesting result that the unstable fixed points turn out to most efficiently drive the logistic map towards a stationary distribution through L.

AB - The thermodynamic length gives a Riemannian metric to a system's phase space. Here we extend the traditional thermodynamic length to the information length (L) out of equilibrium and examine its properties. We utilise L as a useful methodology of analysing non-equilibrium systems without evoking conventional assumptions such as Gaussian statistics, detailed balance, priori-known constraints, or ergodicity and numerically examine how L evolves in time for the logistic map in the chaotic regime depending on initial conditions. To this end, we propose a discrete version of L which is mathematically well defined by taking a set theoretic approach. We identify the areas of phase space where the loss of information of the system takes place most rapidly. In particular, we present an interesting result that the unstable fixed points turn out to most efficiently drive the logistic map towards a stationary distribution through L.

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KW - Non-equilibrium

KW - Relaxation

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Investigation of the statistical distance to reach stationary distributions

Abstract

Bibliographical note

Keywords

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