Information Length Analysis of Linear Autonomous Stochastic Processes
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 <i>n</i>-dimensional linear autonomous stoch...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-11-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/22/11/1265 |
| _version_ | 1797548535703404544 |
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| author | Adrian-Josue Guel-Cortez Eun-jin Kim |
| author_facet | Adrian-Josue Guel-Cortez Eun-jin Kim |
| author_sort | Adrian-Josue Guel-Cortez |
| collection | DOAJ |
| description | 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 <i>n</i>-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 <inline-formula><math display="inline"><semantics><mi>ω</mi></semantics></math></inline-formula>, subject to a damping <inline-formula><math display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula> and a Gaussian white-noise. We explore how the information length depends on <inline-formula><math display="inline"><semantics><mi>ω</mi></semantics></math></inline-formula> and <inline-formula><math display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula>, elucidating the role of critical damping <inline-formula><math display="inline"><semantics><mrow><mi>γ</mi><mo>=</mo><mn>2</mn><mi>ω</mi></mrow></semantics></math></inline-formula> 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. |
| first_indexed | 2024-03-10T15:01:55Z |
| format | Article |
| id | doaj.art-30821139aabb497fba017354d9a41900 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T15:01:55Z |
| publishDate | 2020-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-30821139aabb497fba017354d9a419002023-11-20T20:07:09ZengMDPI AGEntropy1099-43002020-11-012211126510.3390/e22111265Information Length Analysis of Linear Autonomous Stochastic ProcessesAdrian-Josue Guel-Cortez0Eun-jin Kim1Centre for Fluid and Complex Systems, Coventry University, Priory St, Coventry CV1 5FB, UKCentre for Fluid and Complex Systems, Coventry University, Priory St, Coventry CV1 5FB, UKWhen 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 <i>n</i>-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 <inline-formula><math display="inline"><semantics><mi>ω</mi></semantics></math></inline-formula>, subject to a damping <inline-formula><math display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula> and a Gaussian white-noise. We explore how the information length depends on <inline-formula><math display="inline"><semantics><mi>ω</mi></semantics></math></inline-formula> and <inline-formula><math display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula>, elucidating the role of critical damping <inline-formula><math display="inline"><semantics><mrow><mi>γ</mi><mo>=</mo><mn>2</mn><mi>ω</mi></mrow></semantics></math></inline-formula> 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.https://www.mdpi.com/1099-4300/22/11/1265non-equilibriumstochastic processestime-dependent PDFinformation lengthinformation geometryentropy |
| spellingShingle | Adrian-Josue Guel-Cortez Eun-jin Kim Information Length Analysis of Linear Autonomous Stochastic Processes Entropy non-equilibrium stochastic processes time-dependent PDF information length information geometry entropy |
| title | Information Length Analysis of Linear Autonomous Stochastic Processes |
| title_full | Information Length Analysis of Linear Autonomous Stochastic Processes |
| title_fullStr | Information Length Analysis of Linear Autonomous Stochastic Processes |
| title_full_unstemmed | Information Length Analysis of Linear Autonomous Stochastic Processes |
| title_short | Information Length Analysis of Linear Autonomous Stochastic Processes |
| title_sort | information length analysis of linear autonomous stochastic processes |
| topic | non-equilibrium stochastic processes time-dependent PDF information length information geometry entropy |
| url | https://www.mdpi.com/1099-4300/22/11/1265 |
| work_keys_str_mv | AT adrianjosueguelcortez informationlengthanalysisoflinearautonomousstochasticprocesses AT eunjinkim informationlengthanalysisoflinearautonomousstochasticprocesses |