Caratheodory II: The Geometry of Financial Irreversibility

TL;DR

This paper explores the geometric structure underlying financial irreversibility, linking concepts from quantum mechanics to finance, and identifies a measurable asymmetry in state space that relates to fundamental economic principles.

Contribution

It introduces a projective geometric framework for financial irreversibility, revealing a measurable cubic asymmetry analogous to quantum spin systems.

Findings

Identification of a measurable cubic term in the geometry of state space.

Connection between geometric asymmetry and the Second Law of thermodynamics.

Implications for understanding the limitations of traders and the Second Law in finance.

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.