Intrinsic Attractive and Repulsive Interactions: From Classical to Quantum Gases in the Generalized Maxwell-Boltzmann Distribution
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909956842717184 |
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| author | Seifi, Maryam Ebadi, Zahra Agahi, Hamzeh Mehri-Dehnavi, Hossein Mohammadzadeh, Hosein |
| author_facet | Seifi, Maryam Ebadi, Zahra Agahi, Hamzeh Mehri-Dehnavi, Hossein Mohammadzadeh, Hosein |
| contents | The thermodynamic parameter space is flat for an ideal classical gas with non-interacting particles. In contrast, for an ideal quantum Bose (Fermi) gas, the thermodynamic curvature is positive (negative), indicating intrinsic attractive (repulsive) interactions. We generalize the classical Maxwell-Boltzmann distribution by employing a generalized form of the exponential function, proposing the Mittag-Leffler Maxwell-Boltzmann distribution within the framework of superstatistics. We demonstrate that the generalization parameter, $α$, quantifies the statistical interaction. When $α= 1$, the distribution coincides with the standard classical Maxwell-Boltzmann distribution, where no statistical interaction is present. For $0 < α< 1$ ($α> 1$), the statistical interaction is repulsive (attractive), corresponding to a negative (positive) thermodynamic curvature of the system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_03486 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Intrinsic Attractive and Repulsive Interactions: From Classical to Quantum Gases in the Generalized Maxwell-Boltzmann Distribution Seifi, Maryam Ebadi, Zahra Agahi, Hamzeh Mehri-Dehnavi, Hossein Mohammadzadeh, Hosein Statistical Mechanics The thermodynamic parameter space is flat for an ideal classical gas with non-interacting particles. In contrast, for an ideal quantum Bose (Fermi) gas, the thermodynamic curvature is positive (negative), indicating intrinsic attractive (repulsive) interactions. We generalize the classical Maxwell-Boltzmann distribution by employing a generalized form of the exponential function, proposing the Mittag-Leffler Maxwell-Boltzmann distribution within the framework of superstatistics. We demonstrate that the generalization parameter, $α$, quantifies the statistical interaction. When $α= 1$, the distribution coincides with the standard classical Maxwell-Boltzmann distribution, where no statistical interaction is present. For $0 < α< 1$ ($α> 1$), the statistical interaction is repulsive (attractive), corresponding to a negative (positive) thermodynamic curvature of the system. |
| title | Intrinsic Attractive and Repulsive Interactions: From Classical to Quantum Gases in the Generalized Maxwell-Boltzmann Distribution |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2505.03486 |