Defining the Entropy and Internal Energy of a Monetary Schelling model through the Energy States of Individual Agents

This work investigates a modified Schelling model within the scope and aims of Social Physics. The main purpose is to see if how the concepts of potential and kinetic energy can be represented within a computational sociological system. A monetary value is assigned to all the agents in the Monetary Schelling model and a set of dynamics for how the money is spent upon agent position changes and gradual loss. The introduction of the potential and kinetic energy allows for the entropy to be calculated based upon the distribution of the agent energies and as well as the internal energy of the system at each time point. The results show how the movements of the agents produce identity satisfactions with their neighbors decreasing the internal energy of the system along with the decay in the monetary holdings. Simulations are run where agents are provided monetary values at fixed intervals and this causes a subset of the agents to mobilize and explore new positions for satisfaction and increases the entropy with the internal energy removing the system from the fixed point.