Incorporating a monetary variable into the Schelling model addresses the issue of a decreasing entropy trace

The Schelling model of segregation has been shown to have a simulation trace which decreases the entropy of its states as the aggregate number of residential agents surrounded by a threshold of equally labeled agents increases. This introduces a paradox which goes against the second law of thermodynamics that states how entropy must increase. In the efforts to bring principles of physics into the modeling of sociological phenomena this must be addressed. A modification of the model is introduced where a monetary variable is provided to the residential agents (sampled from reported income data), and a dynamic which acts upon this variable when an agent changes its location on the grid. The entropy of the simulation over the iterations is estimated in terms of the aggregate residential homogeneity and the aggregate income homogeneity. The dynamic on the monetary variable shows that it can increase the entropy of the states over the simulation. The path of the traces with both variables in the results show that the shape of the region of entropy is followed supporting that the decrease of entropy due to the residential clustering has a parallel and independent effect increasing the entropy via the monetary variable.