Caratheodory, Finite Resources and the Geometry of Arbitrage

Abstract: Caratheodory's axiom of adiabatic inaccessibility states that, in any neighborhood of a thermodynamic state, certain states remain unreachable via adiabatic processes. Non-arbitrage mirrors this topological restriction in finance. Preserving this constraint in resource-limited systems identifies the exponential family not as a modeling convenience but as the requisite geometric structure unifying both domains.