Metriplectic dynamical systems on contact manifolds
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866913108196327424 |
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| author | Morrison, Philip J. Oh, Yong-Geun |
| author_facet | Morrison, Philip J. Oh, Yong-Geun |
| contents | Flows on symplectic, Poisson, contact, and metriplectic manifolds are reviewed in order to describe our main result, which is to associate a natural metriplectic dynamical system on the general one-jet bundle $J^1N=T^*N\times \mathbb{R}$, which is at once a (trivial) Poisson manifold and a contact manifold. Unlike the standard contact Hamiltonian system, our metriplectic system is thermodynamically consistent in that $$\dot{H} = 0 \quad\mathrm{and}\quad \dot{S} \geq 0$$ under the flow. Here $H$ is the Hamiltonian, while $S$ is the entropy function which is nothing but the $\mathbb{R}$ coordinate function of $J^1N$. As an example we derive the Duffing equation (autonomous and nonautonomous versions) either as a contact Hamiltonian system or as a metriplectic system. We show that for both systems the Duffing equation is a subsystem of three dimensional systems that contain a thermodynamic component, a form that facilitates asymptotic stability analysis of the relevant equilibrium state. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_09482 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Metriplectic dynamical systems on contact manifolds Morrison, Philip J. Oh, Yong-Geun Symplectic Geometry Mathematical Physics Differential Geometry Dynamical Systems Flows on symplectic, Poisson, contact, and metriplectic manifolds are reviewed in order to describe our main result, which is to associate a natural metriplectic dynamical system on the general one-jet bundle $J^1N=T^*N\times \mathbb{R}$, which is at once a (trivial) Poisson manifold and a contact manifold. Unlike the standard contact Hamiltonian system, our metriplectic system is thermodynamically consistent in that $$\dot{H} = 0 \quad\mathrm{and}\quad \dot{S} \geq 0$$ under the flow. Here $H$ is the Hamiltonian, while $S$ is the entropy function which is nothing but the $\mathbb{R}$ coordinate function of $J^1N$. As an example we derive the Duffing equation (autonomous and nonautonomous versions) either as a contact Hamiltonian system or as a metriplectic system. We show that for both systems the Duffing equation is a subsystem of three dimensional systems that contain a thermodynamic component, a form that facilitates asymptotic stability analysis of the relevant equilibrium state. |
| title | Metriplectic dynamical systems on contact manifolds |
| topic | Symplectic Geometry Mathematical Physics Differential Geometry Dynamical Systems |
| url | https://arxiv.org/abs/2605.09482 |