Information Entropy of the Financial Market: Modelling Random Processes Using Open Quantum Systems

Paper: arXiv 2406.20027

Authors: Will Hicks

Abstract

We discuss the role of information entropy on the behaviour of random processes, and how this might take effect in the dynamics of financial market prices. We then go on to show how the Open Quantum Systems approach can be used as a more flexible alternative to classical methods in terms of modelling the entropy gain of a random process. We start by describing an open quantum system that can be used to model the state of a financial market. We then go on to show how to represent an essentially classical diffusion in this framework. Finally, we show how by relaxing certain assumptions, one can generate interesting and essentially non-classical results, which are highlighted through numerical simulations.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 1.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a formal quantum mathematical framework using Hilbert spaces, density matrices, and Von-Neumann entropy to model financial market dynamics and information loss. However, it lacks empirical validation, backtesting, or real market dataset analysis, remaining purely theoretical with stylized numerical simulations.

Research Flowchart

  flowchart TD
    A["Research Goal: Model market entropy & price dynamics via Open Quantum Systems (OQS)"] --> B["Framework Setup: Define market states as an OQS"]
    B --> C["Input: Classical diffusion processes & financial market parameters"]
    C --> D["Computational Engine: Simulate density matrix evolution & entropy gain"]
    D --> E["Assumption Relaxation: Introduce non-Markovian/quantum effects"]
    E --> F["Numerical Simulations: Multi-asset dynamics & non-classical behaviors"]
    F --> G["Key Outcome: Flexible OQS model capturing complex market entropy beyond classical limits"]