Paper: arXiv 2505.01284

Authors: Will Hicks

Abstract

We start with the idea that open quantum systems can be used to represent financial markets by modelling events from the external environment and their impact on the market price. We show how to characterize distinct orbits of the time evolution, and look at the development of the reduced density matrix, that represents the state of the market, over long time frames. In particular we distinguish between classical and non-classical modes of time evolution. We show that whilst both tend to the same set of maximum entropy states, this occurs faster in classical systems, with a knock on effect on the resulting probability distributions. We demonstrate how non-classical modes of time-evolution can be used to incorporate factors such as illiquid trades and imperfect trading mechanisms, and distinguish between different mechanisms of non-classical time evolution.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous theoretical framework using open quantum systems, density matrices, and GKS master equations to model market imperfections. However, it is entirely theoretical with no empirical backtesting, real market data analysis, or reproducible code provided in the text.

Research Flowchart

  flowchart TD
    A[Research Goal: Model Financial Market Imperfections via Open Quantum Systems] --> B[Core Methodology: Model Market State as Reduced Density Matrix]
    B --> C[Inputs: Incorporate Environmental Events, Illiquid Trades & Imperfect Mechanisms]
    C --> D[Compute Time Evolution: Compare Classical vs. Non-Classical Modes]
    D --> E[Outcome 1: Both Modes Tend to Maximum Entropy States]
    D --> F[Outcome 2: Non-Classical Evolution Shows Slower Convergence & Altered Distributions]