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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.16757 |
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| _version_ | 1866910864706109440 |
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| author | Krisut, Paradon Yoo-Kong, Sikarin |
| author_facet | Krisut, Paradon Yoo-Kong, Sikarin |
| contents | The Tsallis entropy, which possesses non-extensive property, is derived from the first principle employing the non-extensive Hamiltonian or the $q$-deformed Hamiltonian with the canonical ensemble assumption in statistical mechanics. Here, the $q$-algebra and properties of $q$-deformed functions are extensively used throughout the derivation. Consequently, the thermodynamic quantities, e.g. internal energy and Helmholtz free energy, are derived and they inheritly exhibit the non-extensiveness. From this intriguing connection between Tasllis entropy and the $q$-deformed Hamiltonian, the parameter $q$ encapsulates the intrinsic degree of non-extensivity for the thermodynamic systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_16757 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Deriving Tsallis entropy from non-extensive Hamiltonian within a statistical mechanics framework Krisut, Paradon Yoo-Kong, Sikarin Statistical Mechanics The Tsallis entropy, which possesses non-extensive property, is derived from the first principle employing the non-extensive Hamiltonian or the $q$-deformed Hamiltonian with the canonical ensemble assumption in statistical mechanics. Here, the $q$-algebra and properties of $q$-deformed functions are extensively used throughout the derivation. Consequently, the thermodynamic quantities, e.g. internal energy and Helmholtz free energy, are derived and they inheritly exhibit the non-extensiveness. From this intriguing connection between Tasllis entropy and the $q$-deformed Hamiltonian, the parameter $q$ encapsulates the intrinsic degree of non-extensivity for the thermodynamic systems. |
| title | Deriving Tsallis entropy from non-extensive Hamiltonian within a statistical mechanics framework |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2411.16757 |