The Rarefaction Paradigm: A Unifying Thermodynamic Topology of Jet, Rocket, and Ion Propulsion via Active Exergy Sinks

This manuscript introduces a paradigm-shifting unification of aerospace propulsion by redefining engines fundamentally as active topological exergy sinks. While classical momentum theory treats propulsion as a downstream reactive consequence, this work mathematically proves that primary physical causality resides in the localized rarefaction field (ΔP). By rigorously combining Navier-Stokes integral formulations with Second-Law exergy balances, we introduce a novel dimensionless metric—the Propulsive Rarefaction Number (Rp)—which uniquely classifies all propulsive systems from scramjets to chemical rockets. Under typical turbofan cruise conditions, rarefaction dictates 68–82% of flow availability (Rp ≫ 1). High-fidelity Monte Carlo simulations (N=10⁴) and Sobol' global sensitivity mapping confirm that topological suction governs over 75% of thrust variance. This deterministic framework is robustly validated via Bayesian Uncertainty Quantification (UQ) against cycle-scaled EASA certification data for the CFM56-5C, achieving an exceptional 0.2% predictive error. Beyond classical aerodynamics, this causal isomorphism resolves boundary-layer ingestion (BLI) paradoxes, predicting realistic power-saving coefficients of 7–12%. Crucially, we demonstrate that this topological rarefaction framework extends universally: mapping fluid pressure deficits (ΔP) directly to both thermodynamic vacuum expansion in chemical rockets and electrostatic potential deficits (ΔV) in ion/plasma thrusters. All derivations, statistical protocols, and reproducible Python models are entirely self-contained.