Legendre Transformation under Micro Canonical Ensemble
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arXiv
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| Auteurs principaux: | , , , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909159884062720 |
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| author | Wu, Jingxu Li, Chenjia Lei, Zhenzhou Wumaier, Tuerdi Li, Congyu Wang, Yan Wang, Zekun |
| author_facet | Wu, Jingxu Li, Chenjia Lei, Zhenzhou Wumaier, Tuerdi Li, Congyu Wang, Yan Wang, Zekun |
| contents | The Legendre transformation is a crucial tool in theoretical physics, known for its symmetry, especially when applied to multivariate functions. In statistical mechanics, ensembles represent the central focus. Leveraging the dimensionless aspect of Legendre transformation, this paper explores the transformation process from the entropy characteristic function of microcanonical ensembles to the analogous definition of partition function transformation. Additionally, it derives characteristic functions, partition functions, and establishes their interrelations, along with deriving corresponding thermodynamic formulas for various ensembles. This streamlined approach sheds light on the fundamental principles of statistical mechanics and underscores the symmetry inherent in Legendre transformation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_02829 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Legendre Transformation under Micro Canonical Ensemble Wu, Jingxu Li, Chenjia Lei, Zhenzhou Wumaier, Tuerdi Li, Congyu Wang, Yan Wang, Zekun Statistical Mechanics Mathematical Physics The Legendre transformation is a crucial tool in theoretical physics, known for its symmetry, especially when applied to multivariate functions. In statistical mechanics, ensembles represent the central focus. Leveraging the dimensionless aspect of Legendre transformation, this paper explores the transformation process from the entropy characteristic function of microcanonical ensembles to the analogous definition of partition function transformation. Additionally, it derives characteristic functions, partition functions, and establishes their interrelations, along with deriving corresponding thermodynamic formulas for various ensembles. This streamlined approach sheds light on the fundamental principles of statistical mechanics and underscores the symmetry inherent in Legendre transformation. |
| title | Legendre Transformation under Micro Canonical Ensemble |
| topic | Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2404.02829 |