The Energy Cohesion Model (ECM): A Unified Inversion Framework for Extracting Cohesion Energies, Cross-Interactions, and Composition in Gas Mixtures

The Energy Cohesion Model (ECM): A Unified Inversion Framework for Extracting Cohesion Energies, Cross-Interactions, and Composition in Gas Mixtures Jae Un Kim November 13, 2025 Abstract The Energy Cohesion Model (ECM) provides a unified, experimentally grounded inversion framework for extracting molecular cohesion energies in both pure and mixed gas systems. Unlike conventional spectroscopic or potential-based approaches, ECM operates entirely on measurable mechanical energy accounting. The model decomposes the input–output energy difference into four physically meaningful components: (i) intrinsic system losses, (ii) intrinsic cohesion energies of pure species, (iii) compositional contributions in mixtures, and (iv) cross-interaction energy (ICE). We show that all inference tasks—including pure-species cohesion, cross-interaction quantification, unknown-species reconstruction, and unknowncomposition recovery—arise from a single grand inversion principle: the difference between expected linear energy contribution and experimentally measured energy loss. This paper develops the full mathematical structure of ECM, establishes solvability conditions for mixtures with unknown species, and demonstrates that the same inversion principle governs all reconstruction tasks. Applications include CO2capture, industrial gas analysis, impurity detection, and real-time mixture diagnostics. 1 1 Introduction Quantifying cohesion energies between gas molecules remains one of the most challenging tasks in molecular physics. Traditional approaches depend heavily on intermolecular potential models, high-resolution spectroscopy, or computationally intensive simulations. Such methods are highly sensitive to theoretical assumptions and often struggle when applied to real gas mixtures where impurities, turbulence, or unknown species are present. The Energy Cohesion Model (ECM) takes a fundamentally different approach. Rather than relying on microscopic potential landscapes, ECM interprets molecular cohesion as an experimentally recoverable quantity derived from macroscopic mechanical energy loss. This loss can be fully decomposed into system-level dissipation, intrinsic cohesion contributions of each gas species, and cross-interaction effects arising within mixtures. A key insight is that ECM does not approximate molecular behavior directly. Instead, it expresses all unknown quantities in terms of differences between expected linear energy contributions and actual measured energy consumption. This inversion-based perspective allows ECM to recover unknown cohesion energies, quantify cross-interaction structures, reconstruct mixture compositions, and identify unknown gases. 2 Theoretical Foundation: The Grand Inversion Principle Although ECM appears to handle many different tasks, its mathematical structure originates from a single principle: Every unknown physical quantity in a gas system is obtained by subtracting the experimentally measured energy loss from the theoretically expected linear energy contribution. The expected contribution represents the linear combination of pure-species cohesion energies, scaled by composition. The measured quantity is the total mechanical energy loss after removing system baseline dissipation. Their difference produces: •pure-species cohesion energies, •mixture cohesion deviation, •cross-interaction energy (ICE), •unknown-species cohesion, 2 •unknown mixture composition. Thus, ECM is not a collection of separate methods. It is a single inversion framework where all results follow from the same algebraic mechanism. 3 Energy Decomposition Framework When energy is injected into a gas system, the total loss satisfies: Einput =Esystem + n X i=1 xiEi+EICE.(1) The measurable quantity is: Eloss =Einput −Eoutput.(2) Thus the mixture energy contribution becomes: Emix =Eloss −Esystem.(3) 3.1 System Baseline Loss System loss is defined experimentally: Esystem = lim Einput→0(Einput −Eoutput).(4) This represents device friction, geometry-induced dissipation, and turbulence unrelated to molecular cohesion. Once determined, it remains constant across all experiments. 4 Pure-Species Cohesion Extraction For a single gas species, composition is trivial: x1= 1. Substituting into Eq. (3) yields: E1=Eloss −Esystem.(5) This is the simplest manifestation of the inversion principle. 3 Table 1: Definition of variables used in the Energy Cohesion Model (ECM). Symbol Physical Meaning Einput Injected mechanical energy into the gas system Eoutput Remaining mechanical energy after gas interaction Eloss Total energy loss: Einput −Eoutput Esystem Baseline device + flow loss, independent of composition Emix Mixture-induced energy consumption (after subtracting baseline) xiMole fraction of species iin the mixture EiIntrinsic cohesion energy of pure gas species i EICE Cross-interaction energy (nonlinear, multi-species term) EuUnknown cohesion energy of an unidentified species ∆EjEffective mixture energy for experiment j XComposition matrix for multi-experiment reconstruction EuVector of unknown cohesion energies 5 Cross-Interaction Energy (ICE) For known mixture composition {xi}, the expected linear cohesion term is: Eexpected =X i xiEi.(6) Using Eq. (3), the cross-interaction energy is: EICE =Emix −X i xiEi.(7) If EICE >0, the mixture exhibits additional cohesive or clustering behavior not captured by simple superposition. 6 Unknown Species Reconstruction 6.1 Single Unknown Gas If species uhas unknown cohesion energy Eu: Eu=Emix −EICE −Pk=uxkEk xu .(8) 6.2 Multiple Unknown Gases With Nunknown gases, perform Nexperiments with different compositions: 4 XEu=∆E. Here, ∆Ej=Emix,j −EICE,j,(9) Xj,i =xj,ui.(10) If Xis full rank, all unknown cohesion energies are uniquely recoverable. 7 Unknown Composition Reconstruction Even when composition is entirely unknown, ECM reconstructs it by repeating the experiment under different conditions. The system becomes: Emix,j =X i xiEi+EICE,j.(11) Together with the constraint: X i xi= 1, xi≥0,(12) composition becomes solvable. 8 Interpretation and Physical Meaning The ICE term represents: •attractive/repulsive interactions, •impurity-induced deviations, •multi-body cohesion, •turbulence-enhanced clustering effects. Meanwhile, Eireflects intrinsic binding tendencies determined purely from experimental macroscopic energy consumption. The unification arises because all extracted quantities— Ei,xi,EICE, and Eunknown— come from the same inversion structure. 5 Table 2: Comparison of analytical paradigms Method Basis Requirements Mass Spectrometry Mass-to-charge separation Vacuum environment, detectors Gas Chromatography Retention-time separation Columns, carriers, separation media IR Spectroscopy Molecular absorption peaks Optical calibration, transmissive window ECM Energy absorption and conservation One controlled input–output measurement 9 Applications •CO2capture monitoring •High-purity gas production •Industrial mixture analysis •Impurity detection •Safety diagnostics for explosive mixtures 10 Conclusion ECM establishes a unified, experimentally accessible inversion framework for quantifying cohesion energies, cross-interactions, and compositions in gas mixtures. All inference steps follow from the same principle—subtracting measured energy from expected linear contribution— making ECM a powerful yet simple tool for real-gas diagnostics. 6