Caratheodory II: The Geometry of Financial Irreversibility

Abstract

In quantum mechanics and finance, numeraire invariance - the unobservability of absolute phase or price scale - fits with a projective and curved state space. This projective geometry has a measurable signature. For spin-one and higher spin systems, the Taylor expansion of directed distance contains a non-zero cubic term, which induces a fundamental asymmetry under the exchange of states. The Second Law, the failure of Maxwell's demon, and the limitations of sequential traders can all be reduced to this asymmetry.