Metriplectic formulations of variational thermodynamics
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909619078561792 |
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| author | Carlier, Valentin |
| author_facet | Carlier, Valentin |
| contents | We propose a metriplectic reformulation of Lagrangian variational formulations for non-equilibrium thermodynamics. We prove that solutions to these constrained variational principles can be generated by the sum of a classic Poisson bracket and a metriplectic 4-bracket, that takes the Hamiltonian and the entropy as generators. We study different cases: simple systems, discrete systems, Euler-Poincaré reduced systems and systems with no symplectic part. Several example are shown, including infinite dimensional problems arising from continuum mechanics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_11558 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Metriplectic formulations of variational thermodynamics Carlier, Valentin Mathematical Physics 80A05 (Primary), 76A02 We propose a metriplectic reformulation of Lagrangian variational formulations for non-equilibrium thermodynamics. We prove that solutions to these constrained variational principles can be generated by the sum of a classic Poisson bracket and a metriplectic 4-bracket, that takes the Hamiltonian and the entropy as generators. We study different cases: simple systems, discrete systems, Euler-Poincaré reduced systems and systems with no symplectic part. Several example are shown, including infinite dimensional problems arising from continuum mechanics. |
| title | Metriplectic formulations of variational thermodynamics |
| topic | Mathematical Physics 80A05 (Primary), 76A02 |
| url | https://arxiv.org/abs/2410.11558 |