Information Length Analysis of Linear Autonomous Stochastic Processes

• Published in: Entropy (Basel, Switzerland) Vol. 22; no. 11; p. 1265
• Main Authors: Guel-Cortez, Adrian-Josue, Kim, Eun-jin
• Format: Journal Article
• Language: English
• Published: Switzerland MDPI 07.11.2020; MDPI AG
• Subjects: entropy; information geometry; information length; non-equilibrium; stochastic processes; time-dependent PDF; entropy; information geometry; fluctuations; time-dependent PDF; non-equilibrium; stochastic processes; information length
• ISSN: 1099-4300; 1099-4300
• DOI: 10.3390/e22111265

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.