A closer look at the chemical potential of an ideal agent system

ArXiv ID: 2401.09233 “View on arXiv”

Authors: Unknown

Abstract

Models for spin systems known from statistical physics are used in econometrics in the form of agent-based models. Econophysics research in econometrics is increasingly developing general market models that describe exchange phenomena and use the chemical potential $μ$ known from physics in the context of particle number changes. In statistical physics, equations of state are known for the chemical potential, which take into account the respective model framework and the corresponding state variables. A simple transfer of these equations of state to problems in econophysics appears difficult. To the best of our knowledge, the equation of state for the chemical potential is currently missing even for the simplest conceivable model of an ideal agent system. In this paper, this research gap is closed and the equation of state for the chemical potential is derived from the econophysical model assumptions of the ideal agent system. An interpretation of the equation of state leads to fundamental relationships that could also have been guessed, but are shown here by the theory.

Keywords: Econophysics, Agent-Based Models, Statistical Physics, Chemical Potential, Ideal Agent System, General Equilibrium / Market Models

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats
• Why: The paper is heavy on theoretical physics derivations using statistical mechanics concepts like chemical potential and grand canonical ensembles, indicating high mathematical complexity. However, it lacks any empirical data, backtests, or implementation details, focusing purely on theoretical model derivation.

  flowchart TD
    A["Research Goal<br>Derive chemical potential<br>equation of state for<br>ideal agent system"] --> B["Methodology<br>Statistical Physics<br>Agent-Based Modeling"]
    B --> C["Model Setup<br>Define Ideal Agent System<br>State Variables"]
    C --> D["Computational Process<br>Derive Partition Function<br>& Grand Canonical Ensemble"]
    D --> E["Mathematical Derivation<br>Calculate chemical potential μ<br>Via thermodynamic relation"]
    E --> F["Key Findings<br>Equation of State for μ<br>Validated fundamental relationships<br>Closed research gap"]