Investigation of the statistical distance to reach stationary distributions

S. B. Nicholson, Eun Jin Kim

Research output: Contribution to journalArticlepeer-review

28 Citations (Scopus)
26 Downloads (Pure)


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 languageEnglish
Pages (from-to)83-88
Number of pages6
JournalPhysics Letters A
Issue number3
Early online date7 Nov 2014
Publication statusPublished - 23 Jan 2015
Externally publishedYes

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


  • Logistic map
  • Non-equilibrium
  • Relaxation
  • Thermodynamic length

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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