We derive the irreversible increase of the spatial-to-material ratio from the UD field equations. The conditional asymmetry of the U and D attributes—U expands unconditionally while D condenses only above the threshold α—is shown to imply UU/UU > DD/DD on global scales. From this inequality and the global constraint E = C, we prove strictly that the global entropy S (UU+UD) / (DD+DU) satisfies S > 0. For local isolated systems, the same field equations force the entropy to converge to unity, with the approach direction determined by the initial E/C ratio. The ideal gas law and the equipartition theorem are derived from UD momentum transfer, giving the temperature calibration T ₓ₇=T₀ E/C with T₀=2mc^2/3k₁. For a multi-species gas at thermal equilibrium, heavier particles have smaller E/C. Apparent local entropy decrease during structure formation is quantified. This work supplements classical thermodynamics with a first-principles field-theoretic foundation. All results follow from the UD axioms without adjustable parameters.
Dan Zhu (Sun,) studied this question.