Thermodynamics Mathematics

These pages develop ordered composition and scalable compounds, local Pfaff geometry, convex contact sectors and entropy calibration. Ensemble constructions, mixture dynamics, continuum pressure, spatial measure and information provide further analytic prerequisites. The results specify the mathematical assumptions needed for each construction, including local regularity, admissibility, integrability and any choice principle. Their physical interpretation belongs to the corresponding thermodynamics pages and does not enter the mathematical proofs.

Each main page introduces the objects and assumptions needed for its results, with links to the prerequisites used in the exposition. Its examples companion gives concrete calculations, limiting cases or counterexamples that clarify those hypotheses. Follow prerequisite links when a definition or earlier result is needed, and read the stated scope alongside each conclusion. Local statements distinguish assumptions from deductions and keep the conventions used in calculations visible. The page list below provides entry points into the subject; the order follows the planned progression from foundational definitions to the later applications.

• Ordered Composition
• Nonsmooth Equilibrium
• Local Pfaff Geometry
• Convex Contact And Mixing
• Ensembles And Limits
• Mixture Dynamics And Shells
• Continuum Pressure
• Spatial Measure And Information
• Interacting Ensemble Geometry