Statistical Mechanics as an Admissibility System

This paper interprets statistical mechanics through the admissibility framework of the Paton System. Instead of treating statistical behaviour purely as a probabilistic distribution of microstates, the framework recognises that only states satisfying the governing constraints of a system are structurally permitted. Microstates therefore correspond to admissible configurations within a constrained state space. Macrostates emerge as statistical aggregates over regions of admissible states, while equilibrium represents stable continuation inside a maximally admissible region. This interpretation clarifies why statistical regularities appear across physical systems: they arise from constraint-defined admissible geometry prior to probabilistic modelling. The work positions statistical mechanics as a structural description of admissible configuration regions under governing constraints rather than unrestricted probabilistic variation.