The Ontology of Inverse Entropy: Order Creation as Constraint Formation

Entropy increases. Yet life, cognition, and civilization persistently create order. What is the fundamental nature of this order creation? In Energy-Efficiency Theory (EET), the answer is rooted in the same mechanism that drives entropy increase: constraint transitions. Entropy increase is the spontaneous meltdown of constraints (Ebᵐᵉˡᵗ crossed). Inverse entropy—order creation—is the active formation of new constraints (Ebᶠᵒʳᵐ crossed) through the investment of free-state energy. This paper develops the ontology of inverse entropy from the generative foundations of EET Core Rules v5.0. We define inverse entropy Ṡᵢₙᵥ as the rate of constraint formation, driven by directed investment of formation power Ėform. From capacity geometry, the cooperative capacity Γ(η) = Cₘ Cᵣ ∝ 1 - x² governs the efficiency of constraint formation: at η=1, Γ is maximal. The inverse entropy rate is:\[Ṡᵢₙᵥ = Γ(η) · {Ėform}{Teff},\]where Teff is the effective temperature. We distinguish thermal and active formation regimes, and establish the hierarchical scaling Ṡᵢₙᵥ ∝ Lα (α ≈ 0.6), unifying order creation from molecular to civilizational scales. Falsifiable predictions include the correlation between brain free power and learning rate, superlinear scaling of innovation with R&D investment, and temperature dependence of ectotherm learning. This version adds explicit interfaces to Motion and Force (F = Teff ∇ Sᵢₙᵥ), Inertia (creation vs. preservation), and Time (local reversal), and a comprehensive appendix of 16 deep insights (L3 EXTENDED). Inverse entropy completes the EET thermodynamic trilogy: Entropy (disorder), Inverse Entropy (order creation), and Temperature (fluctuation strength). {Keywords}: Inverse entropy; order creation; constraint formation; capacity geometry; Energy-Efficiency Theory; learning; innovation; civilization