PNMS Mode B — Statistical Mechanics Branch: Φ_R Coupled to the Boltzmann Relation and Thermal Distributions

This document defines the statistical-mechanics branch of the Property-Neutral Matrixscope (PNMS) constructive operation (Mode B). The branch specifies how the PNMS projection operator Φ_R is coupled to thermodynamic relations based on the Boltzmann equation . It identifies the active quantities used in the analysis (thermal energy, temperature, entropy, and Landauer energy), defines the corresponding rows in the PNMS reference basis, and establishes the constraint surface that represents thermal states in signature space. The document also defines the operational sequence used to construct and evaluate thermal states and introduces the statistical-mechanics case studies associated with this branch