The Mesoscopic Partition Function:A Combined Spatial and Phase-Space Cell Structure

Condensed Matter > Statistical Mechanics [Submitted on 1 May 2026 (v1), last revised 30 May 2026 (this version, v2)] Title:The Mesoscopic Partition Function:A Combined Spatial and Phase-Space Cell Structure View PDFAbstract: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. Submission history From: Bob Osano [view email][v1] Fri, 1 May 2026 12:52:42 UTC (12 KB) [v2] Sat, 30 May 2026 12:20:56 UTC (14 KB) Current browse context: cond-mat.stat-mech References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) IArxiv Recommender (What is IArxiv?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.