Caratheodory II: The Geometry of Financial Irreversibility

Paper: arXiv 2603.09966

Authors: Bernhard K Meister

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.

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 1.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides an interesting theoretical bridge between quantum information geometry (spin-1 systems, Veronese submanifolds) and financial market irreversibility via numeraire invariance. However, it is purely conceptual/theoretical with no empirical data, backtesting, or quantitative market validation.

Research Flowchart

  flowchart TD
    A[Research Goal: Explain Financial & Quantum Irreversibility via Numeraire Invariance] --> B[Input: Spin-1+ Systems & Price Scale Invariance]
    B --> C[Method: Model State Space using Projective Geometry]
    C --> D[Compute Taylor Expansion of Directed Distance]
    D --> E[Outcome: Non-Zero Cubic Term Breaks Exchange Symmetry]
    E --> F[Key Findings: Explains Second Law, Maxwell's Demon Failure & Trading Limits]