On the Connection between Temperature and Volatility in Ideal Agent Systems

Paper: arXiv 2303.15164

Authors: Christoph J. Börner, Ingo Hoffmann, John H. Stiebel

Abstract

Models for spin systems known from statistical physics are applied by analogy in econometrics in the form of agent-based models. Researchers suggest that the state variable temperature $T$ corresponds to volatility $σ$ in capital market theory problems. To the best of our knowledge, this has not yet been theoretically derived, for example, for an ideal agent system. In the present paper, we derive the exact algebraic relation between $T$ and $σ$ for an ideal agent system and discuss implications and limitations.

Complexity vs Empirical Score

• Math Complexity: 7.0/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a formal theoretical derivation linking temperature in statistical mechanics to financial volatility within ideal agent systems, addressing a notable gap in econophysics literature. However, it is predominantly a mathematical and conceptual contribution lacking empirical validation or backtesting on real-world market data.

Research Flowchart

  flowchart TD
    A[Research Goal: Derive algebraic relation between Temperature T & Volatility σ] --> B[Input: Ideal Agent System & Statistical Physics Spin Models]
    B --> C[Methodology: Apply Econophysics Analogy to Capital Markets]
    C --> D[Mathematical Derivation of Exact Algebraic Relation T ↔ σ]
    D --> E[Analysis of Model Implications & Limitations]
    E --> F[Outcome: Theoretical Proof connecting Spin System T to Market Volatility σ]