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This work investigates a modified Schelling model within the scope and aimsof Social Physics. The main purpose is to see if how the concepts of potentialand kinetic energy can be represented within a computational sociologicalsystem. A monetary value is assigned to all the agents in the MonetarySchelling model and a set of dynamics for how the money is spent upon agentposition changes and gradual loss. The introduction of the potential andkinetic energy allows for the entropy to be calculated based upon thedistribution of the agent energies and as well as the internal energy of thesystem at each time point. The results show how the movements of the agentsproduce identity satisfactions with their neighbors decreasing the internalenergy of the system along with the decay in the monetary holdings. Simulationsare run where agents are provided monetary values at fixed intervals and thiscauses a subset of the agents to mobilize and explore new positions forsatisfaction and increases the entropy with the internal energy removing thesystem from the fixed point.

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