Temperature Measurement in Agent Systems

ArXiv ID: 2507.08394 “View on arXiv”

Authors: Christoph J. Börner, Ingo Hoffmann

Abstract

Models for spin systems, known from statistical physics, are applied analogously in econometrics in the form of agent-based models. The models discussed in the econophysics literature all use the state variable $T$, which, in physics, represents the temperature of a system. However, there is little evidence on how temperature can be measured in econophysics, so that the models can be applied. Only in idealized capital market applications has the relationship between temperature and volatility been demonstrated, allowing temperature to be determined through volatility measurements. The question remains how this can be achieved in agent systems beyond capital market applications. This paper focuses precisely on this question. It examines an agent system with two decision options in a news environment, establishes the measurement equation, and outlines the basic concept of temperature measurement. The procedure is illustrated using an example. In an application with competing subsystems, an interesting strategy for influencing the average opinion in the competing subsystem is presented.

Keywords: Agent-Based Models, Econophysics, Spin Systems, Temperature Measurement, Market Volatility, Multi-Asset/Agent Systems

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats
  • Why: The paper is deeply mathematical, using advanced statistical physics concepts like the Ising model, mean-field approximation, and thermodynamic definitions to derive measurement equations. However, it lacks any empirical data, backtests, or implementation details, focusing solely on theoretical derivation and an illustrative example.
  flowchart TD
    A["Research Goal<br/>How to measure Temperature<br/>in agent systems?"] --> B["Methodology<br/>Derive Measurement Equation<br/>for News Environment"]
    B --> C["Data Input<br/>Volatility & Market Data"]
    C --> D["Computational Process<br/>Apply Equation &<br/>Calculate Temperature"]
    D --> E["Key Finding 1<br/>Temperature measurable<br/>beyond capital markets"]
    D --> F["Key Finding 2<br/>Strategy to influence<br/>average opinion found"]