Information Length Analysis of Linear Autonomous Stochastic Processes

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Abstract

When studying the behaviour of complex dynamical systems, a statistical formulation can provide useful insights. In particular, information geometry is a promising tool for this purpose. In this paper, we investigate the information length for n-dimensional linear autonomous stochastic processes, providing a basic theoretical framework that can be applied to a large set of problems in engineering and physics. A specific application is made to a harmonically bound particle system with the natural oscillation frequency ω, subject to a damping γ and a Gaussian white-noise. We explore how the information length depends on ω and γ, elucidating the role of critical damping γ = 2ω in information geometry. Furthermore, in the long time limit, we show that the information length reflects the linear geometry associated with the Gaussian statistics in a linear stochastic process.
Original languageEnglish
Article number1265
Pages (from-to)1-18
Number of pages18
JournalEntropy
Volume22
Issue number11
DOIs
Publication statusPublished - 7 Nov 2020

Bibliographical note

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

Funder

Leverhulme Trust Research Fellowship (RF-2018-142-9).

Keywords

  • Entropy
  • Fluctuations
  • Information geometry
  • Information length
  • Non-equilibrium
  • Stochastic processes
  • Time-dependent PDF

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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