Gradient and GENERIC Systems in the Space of Fluxes, Applied to Reacting Particle Systems
In a previous work we devised a framework to derive generalised gradient systems for an evolution equation from the large deviations of an underlying microscopic system, in the spirit of the Onsager–Machlup relations. Of particular interest is the case where the microscopic system consists...
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| Format: | Article |
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MDPI AG
2018-08-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/20/8/596 |
| _version_ | 1828364613620596736 |
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| author | D. R. Michiel Renger |
| author_facet | D. R. Michiel Renger |
| author_sort | D. R. Michiel Renger |
| collection | DOAJ |
| description | In a previous work we devised a framework to derive generalised gradient systems for an evolution equation from the large deviations of an underlying microscopic system, in the spirit of the Onsager–Machlup relations. Of particular interest is the case where the microscopic system consists of random particles, and the macroscopic quantity is the empirical measure or concentration. In this work we take the particle flux as the macroscopic quantity, which is related to the concentration via a continuity equation. By a similar argument the large deviations can induce a generalised gradient or GENERIC system in the space of fluxes. In a general setting we study how flux gradient or GENERIC systems are related to gradient systems of concentrations. This shows that many gradient or GENERIC systems arise from an underlying gradient or GENERIC system where fluxes rather than densities are being driven by (free) energies. The arguments are explained by the example of reacting particle systems, which is later expanded to include spatial diffusion as well. |
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| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-14T05:18:28Z |
| publishDate | 2018-08-01 |
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| spelling | doaj.art-6ccf471f5a5847eeb7f5f293ccce1f3c2022-12-22T02:10:16ZengMDPI AGEntropy1099-43002018-08-0120859610.3390/e20080596e20080596Gradient and GENERIC Systems in the Space of Fluxes, Applied to Reacting Particle SystemsD. R. Michiel Renger0Weierstrass Institute (WIAS), Mohrenstrasse 39, 10117 Berlin, GermanyIn a previous work we devised a framework to derive generalised gradient systems for an evolution equation from the large deviations of an underlying microscopic system, in the spirit of the Onsager–Machlup relations. Of particular interest is the case where the microscopic system consists of random particles, and the macroscopic quantity is the empirical measure or concentration. In this work we take the particle flux as the macroscopic quantity, which is related to the concentration via a continuity equation. By a similar argument the large deviations can induce a generalised gradient or GENERIC system in the space of fluxes. In a general setting we study how flux gradient or GENERIC systems are related to gradient systems of concentrations. This shows that many gradient or GENERIC systems arise from an underlying gradient or GENERIC system where fluxes rather than densities are being driven by (free) energies. The arguments are explained by the example of reacting particle systems, which is later expanded to include spatial diffusion as well.http://www.mdpi.com/1099-4300/20/8/596large deviationsfluxesmacroscopic fluctuation theoryOnsager–Machlupgradient structuresGENERICchemical reaction networks |
| spellingShingle | D. R. Michiel Renger Gradient and GENERIC Systems in the Space of Fluxes, Applied to Reacting Particle Systems Entropy large deviations fluxes macroscopic fluctuation theory Onsager–Machlup gradient structures GENERIC chemical reaction networks |
| title | Gradient and GENERIC Systems in the Space of Fluxes, Applied to Reacting Particle Systems |
| title_full | Gradient and GENERIC Systems in the Space of Fluxes, Applied to Reacting Particle Systems |
| title_fullStr | Gradient and GENERIC Systems in the Space of Fluxes, Applied to Reacting Particle Systems |
| title_full_unstemmed | Gradient and GENERIC Systems in the Space of Fluxes, Applied to Reacting Particle Systems |
| title_short | Gradient and GENERIC Systems in the Space of Fluxes, Applied to Reacting Particle Systems |
| title_sort | gradient and generic systems in the space of fluxes applied to reacting particle systems |
| topic | large deviations fluxes macroscopic fluctuation theory Onsager–Machlup gradient structures GENERIC chemical reaction networks |
| url | http://www.mdpi.com/1099-4300/20/8/596 |
| work_keys_str_mv | AT drmichielrenger gradientandgenericsystemsinthespaceoffluxesappliedtoreactingparticlesystems |