Hamiltonian thermodynamics on symplectic manifolds
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913073753751552 |
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| author | Ghosh, Aritra Harikumar, E. |
| author_facet | Ghosh, Aritra Harikumar, E. |
| contents | We describe a symplectic approach towards thermodynamics in which thermodynamic transformations are described by (symplectic) Hamiltonian dynamics. Upon identifying the spaces of equilibrium states with Lagrangian submanifolds of a symplectic manifold, we present a Hamiltonian description of thermodynamic processes where the space of equilibrium states of a system in a certain ensemble is contained in the level set on which the Hamiltonian assumes a constant value. In particular, we work out two explicit examples involving the ideal gas and then describe a Hamiltonian approach towards constructing maps between related thermodynamic systems, e.g., the ideal (non-interacting) gas and interacting gases. Finally, we extend the theory of symplectic Hamiltonian dynamics to describe (a) the free expansion of the ideal gas which involves irreversible generation of entropy, and (b) a symplectic port-Hamiltonian framework for the ideal gas which is exemplified through two problems, namely, the problem of isothermal expansion against a piston and that of heat transfer between a heat bath and the gas via a thermal conductor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_04622 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hamiltonian thermodynamics on symplectic manifolds Ghosh, Aritra Harikumar, E. Mathematical Physics Statistical Mechanics Symplectic Geometry Classical Physics We describe a symplectic approach towards thermodynamics in which thermodynamic transformations are described by (symplectic) Hamiltonian dynamics. Upon identifying the spaces of equilibrium states with Lagrangian submanifolds of a symplectic manifold, we present a Hamiltonian description of thermodynamic processes where the space of equilibrium states of a system in a certain ensemble is contained in the level set on which the Hamiltonian assumes a constant value. In particular, we work out two explicit examples involving the ideal gas and then describe a Hamiltonian approach towards constructing maps between related thermodynamic systems, e.g., the ideal (non-interacting) gas and interacting gases. Finally, we extend the theory of symplectic Hamiltonian dynamics to describe (a) the free expansion of the ideal gas which involves irreversible generation of entropy, and (b) a symplectic port-Hamiltonian framework for the ideal gas which is exemplified through two problems, namely, the problem of isothermal expansion against a piston and that of heat transfer between a heat bath and the gas via a thermal conductor. |
| title | Hamiltonian thermodynamics on symplectic manifolds |
| topic | Mathematical Physics Statistical Mechanics Symplectic Geometry Classical Physics |
| url | https://arxiv.org/abs/2410.04622 |