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Information Length Analysis of Linear Autonomous Stochastic Processes

Centre for Fluid and Complex Systems, Coventry University, Priory St, Coventry CV1 5FB, UK
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Entropy 2020, 22(11), 1265; https://doi.org/10.3390/e22111265
Received: 7 October 2020 / Revised: 2 November 2020 / Accepted: 5 November 2020 / Published: 7 November 2020
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. View Full-Text
Keywords: non-equilibrium; stochastic processes; time-dependent PDF; information length; information geometry; entropy; fluctuations non-equilibrium; stochastic processes; time-dependent PDF; information length; information geometry; entropy; fluctuations
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MDPI and ACS Style

Guel-Cortez, A.-J.; Kim, E.-j. Information Length Analysis of Linear Autonomous Stochastic Processes. Entropy 2020, 22, 1265. https://doi.org/10.3390/e22111265

AMA Style

Guel-Cortez A-J, Kim E-j. Information Length Analysis of Linear Autonomous Stochastic Processes. Entropy. 2020; 22(11):1265. https://doi.org/10.3390/e22111265

Chicago/Turabian Style

Guel-Cortez, Adrian-Josue; Kim, Eun-jin. 2020. "Information Length Analysis of Linear Autonomous Stochastic Processes" Entropy 22, no. 11: 1265. https://doi.org/10.3390/e22111265

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