Lagrangian formalism and classical statistical ensemble
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866911330127052800 |
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| author | Yoo-Kong, Sikarin |
| author_facet | Yoo-Kong, Sikarin |
| contents | We present a formulation of classical statistical mechanics based on a Lagrangian description on the tangent bundle. In this approach, a Wick rotation from real time to imaginary time is employed as a technical device that facilitates the construction of a Hamiltonian structure expressed in velocity variables. The resulting dynamics preserves a natural measure induced by the associated symplectic form on the tangent bundle. This measure-preserving property enables the consistent definition of classical statistical ensembles directly in terms of Lagrangian variables. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_16288 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Lagrangian formalism and classical statistical ensemble Yoo-Kong, Sikarin Mathematical Physics We present a formulation of classical statistical mechanics based on a Lagrangian description on the tangent bundle. In this approach, a Wick rotation from real time to imaginary time is employed as a technical device that facilitates the construction of a Hamiltonian structure expressed in velocity variables. The resulting dynamics preserves a natural measure induced by the associated symplectic form on the tangent bundle. This measure-preserving property enables the consistent definition of classical statistical ensembles directly in terms of Lagrangian variables. |
| title | Lagrangian formalism and classical statistical ensemble |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2309.16288 |