HARMONIA: A Unified Entropy-Driven Framework for Adsorption and Transport—From Molecular Stochastics to Macroscopic Kinetics

The rigorous design of adsorption-based separation processes, such as Pressure Swing Adsorption (PSA) and Temperature Swing Adsorption (TSA), is fundamentally dependent on the accuracy of the underlying mathematical models describing equilibrium isotherms and transport kinetics. However, the current state of the art is characterized by a fragmentation of theory: a “zoo” of empirical isotherms (Langmuir, BET, Freundlich, Sips) is often coupled with disconnected kinetic laws (LDF, Fickian diffusion) in a manner that lacks thermodynamic consistency. This disconnect frequently leads to numerical instabilities and violations of the Second Law of Thermodynamics in complex reactor simulations. In this work, we introduce HARMONIA, a unified thermodynamic framework based on the minimization of a convex Free Energy functional governed by Orlicz-class entropy. We demonstrate that the classical isotherms are not distinct empirical laws but mathematical limits of a single entropy-driven principle, determined by the microscopic energy landscape of adsorption sites. We validate the framework against experimental high-pressure datasets for CO2 on Co-MOF-74 and cryogenic N2 on Mn-MOF, covering regimes from micropore filling and monolayer adsorption to multilayer growth and gas-phase non-ideality, and we further illustrate its applicability to pH-active sorbents in aqueous phase. Using rigorous non-parametric bootstrap analysis and profile likelihoods, we prove the parameter identifiability of the derived models, extracting physically meaningful enthalpies and micropore volumes together with their confidence intervals and correlation structures. Furthermore, we show that transport kinetics derived from this functional constitute a Wasserstein Gradient Flow, guaranteeing unconditional numerical stability, positivity preservation, and monotonic entropy production. This framework bridges the gap between molecular stochasticity and macroscopic reactor design, offering a robust, thermodynamically consistent tool for the engineering of next-generation separation processes.