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Rate of Entropy Production in Stochastic Mechanical Systems
Entropy production in stochastic mechanical systems is examined here with strict bounds on its rate. Stochastic mechanical systems include pure diffusions in Euclidean space or on Lie groups, as well as systems evolving on phase space for which the fluctuation-dissipation theorem applies, i.e., retu...
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Formato: | Online Artículo Texto |
Lenguaje: | English |
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MDPI
2021
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Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8774488/ https://www.ncbi.nlm.nih.gov/pubmed/35052045 http://dx.doi.org/10.3390/e24010019 |
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author | Chirikjian, Gregory S. |
author_facet | Chirikjian, Gregory S. |
author_sort | Chirikjian, Gregory S. |
collection | PubMed |
description | Entropy production in stochastic mechanical systems is examined here with strict bounds on its rate. Stochastic mechanical systems include pure diffusions in Euclidean space or on Lie groups, as well as systems evolving on phase space for which the fluctuation-dissipation theorem applies, i.e., return-to-equilibrium processes. Two separate ways for ensembles of such mechanical systems forced by noise to reach equilibrium are examined here. First, a restorative potential and damping can be applied, leading to a classical return-to-equilibrium process wherein energy taken out by damping can balance the energy going in from the noise. Second, the process evolves on a compact configuration space (such as random walks on spheres, torsion angles in chain molecules, and rotational Brownian motion) lead to long-time solutions that are constant over the configuration space, regardless of whether or not damping and random forcing balance. This is a kind of potential-free equilibrium distribution resulting from topological constraints. Inertial and noninertial (kinematic) systems are considered. These systems can consist of unconstrained particles or more complex systems with constraints, such as rigid-bodies or linkages. These more complicated systems evolve on Lie groups and model phenomena such as rotational Brownian motion and nonholonomic robotic systems. In all cases, it is shown that the rate of entropy production is closely related to the appropriate concept of Fisher information matrix of the probability density defined by the Fokker–Planck equation. Classical results from information theory are then repurposed to provide computable bounds on the rate of entropy production in stochastic mechanical systems. |
format | Online Article Text |
id | pubmed-8774488 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2021 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-87744882022-01-21 Rate of Entropy Production in Stochastic Mechanical Systems Chirikjian, Gregory S. Entropy (Basel) Article Entropy production in stochastic mechanical systems is examined here with strict bounds on its rate. Stochastic mechanical systems include pure diffusions in Euclidean space or on Lie groups, as well as systems evolving on phase space for which the fluctuation-dissipation theorem applies, i.e., return-to-equilibrium processes. Two separate ways for ensembles of such mechanical systems forced by noise to reach equilibrium are examined here. First, a restorative potential and damping can be applied, leading to a classical return-to-equilibrium process wherein energy taken out by damping can balance the energy going in from the noise. Second, the process evolves on a compact configuration space (such as random walks on spheres, torsion angles in chain molecules, and rotational Brownian motion) lead to long-time solutions that are constant over the configuration space, regardless of whether or not damping and random forcing balance. This is a kind of potential-free equilibrium distribution resulting from topological constraints. Inertial and noninertial (kinematic) systems are considered. These systems can consist of unconstrained particles or more complex systems with constraints, such as rigid-bodies or linkages. These more complicated systems evolve on Lie groups and model phenomena such as rotational Brownian motion and nonholonomic robotic systems. In all cases, it is shown that the rate of entropy production is closely related to the appropriate concept of Fisher information matrix of the probability density defined by the Fokker–Planck equation. Classical results from information theory are then repurposed to provide computable bounds on the rate of entropy production in stochastic mechanical systems. MDPI 2021-12-23 /pmc/articles/PMC8774488/ /pubmed/35052045 http://dx.doi.org/10.3390/e24010019 Text en © 2021 by the author. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Chirikjian, Gregory S. Rate of Entropy Production in Stochastic Mechanical Systems |
title | Rate of Entropy Production in Stochastic Mechanical Systems |
title_full | Rate of Entropy Production in Stochastic Mechanical Systems |
title_fullStr | Rate of Entropy Production in Stochastic Mechanical Systems |
title_full_unstemmed | Rate of Entropy Production in Stochastic Mechanical Systems |
title_short | Rate of Entropy Production in Stochastic Mechanical Systems |
title_sort | rate of entropy production in stochastic mechanical systems |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8774488/ https://www.ncbi.nlm.nih.gov/pubmed/35052045 http://dx.doi.org/10.3390/e24010019 |
work_keys_str_mv | AT chirikjiangregorys rateofentropyproductioninstochasticmechanicalsystems |