Thermodynamic Relativity in Macro-Healthcare Systems: A Unified Isomorphic Geometric Framework for Throughput, Spacetime Curvature, and Global Operational Models

This paper introduces a novel macro-strategic and systems engineering framework that maps healthcare delivery networks using a unified thermodynamic-relativistic isomorphism. Rather than treating physical metaphors as purely illustrative analogies, we formalize macro-healthcare dynamics by deriving a localized line element, constructing an explicit metric tensor, and coupling non-linear nuclear reactor kinetics with modified gravitational field equations. Patient demand is formalized as a non-compressible, high-pressure kinetic fluid, clinical capacity as an effective active mass warped by social care bottlenecks (static mass), and macro-level queuing systems as a form of geometric time dilation. We apply this framework to analyze the operational invariants of three global paradigms: the United Kingdom's National Health Service (NHS), the United States healthcare market, and Australia's dual-track Medicare system. The resulting equations convert soft human-resource constraints into hard, non-linear geometric boundaries, providing a robust mathematical foundation for predicting asset locking, cascading regional collapses, and structural workforce breakdown.