Investigating information geometry in classical and quantum systems through information length

Research output: Contribution to journalArticle

12 Citations (Scopus)
6 Downloads (Pure)

Abstract

Stochastic processes are ubiquitous in nature and laboratories, and play a major role across traditional disciplinary boundaries. These stochastic processes are described by different variables and are thus very system-specific. In order to elucidate underlying principles governing different phenomena, it is extremely valuable to utilise a mathematical tool that is not specific to a particular system. We provide such a tool based on information geometry by quantifying the similarity and disparity between Probability Density Functions (PDFs) by a metric such that the distance between two PDFs increases with the disparity between them. Specifically, we invoke the information length L(t) to quantify information change associated with a time-dependent PDF that depends on time. L(t) is uniquely defined as a function of time for a given initial condition. We demonstrate the utility of L(t) in understanding information change and attractor structure in classical and quantum systems.

Original languageEnglish
Article number574
JournalEntropy
Volume20
Issue number8
DOIs
Publication statusPublished - 3 Aug 2018
Externally publishedYes

Keywords

  • Attractor
  • Chaos
  • Fisher information
  • Fokker-Planck equation
  • Information length
  • Langevin equation
  • Probability density function
  • Relaxation
  • Stochastic processes

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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