The Mesoscopic Partition Function:A Combined Spatial and Phase-Space Cell Structure
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866914620173713408 |
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| author | Osano, Bob |
| author_facet | Osano, Bob |
| contents | We develop a mesoscopic formulation of equilibrium statistical mechanics based on coarse-grained occupation-number sectors of one-particle phase space. A mesoscopic partition function is constructed by averaging the microscopic Hamiltonian over configurations compatible with a given occupation profile. The construction converges to the canonical Gibbs partition function in the fine-graining limit and remains compatible with interacting many-body systems. Within this framework, thermodynamic extensivity is shown to be equivalent to asymptotic factorisation of the mesoscopic partition function, while residual inter-cell correlations generate subextensive corrections. The resulting formalism provides a mathematically consistent bridge between microscopic Gibbs theory and mesoscopic thermodynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_00958 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Mesoscopic Partition Function:A Combined Spatial and Phase-Space Cell Structure Osano, Bob Statistical Mechanics Mathematical Physics We develop a mesoscopic formulation of equilibrium statistical mechanics based on coarse-grained occupation-number sectors of one-particle phase space. A mesoscopic partition function is constructed by averaging the microscopic Hamiltonian over configurations compatible with a given occupation profile. The construction converges to the canonical Gibbs partition function in the fine-graining limit and remains compatible with interacting many-body systems. Within this framework, thermodynamic extensivity is shown to be equivalent to asymptotic factorisation of the mesoscopic partition function, while residual inter-cell correlations generate subextensive corrections. The resulting formalism provides a mathematically consistent bridge between microscopic Gibbs theory and mesoscopic thermodynamics. |
| title | The Mesoscopic Partition Function:A Combined Spatial and Phase-Space Cell Structure |
| topic | Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2605.00958 |