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

published in Nature Scientific Reports: https://rdcu.be/b8opG

part of the collection on Socialphysics: https://www.nature.com/collections/hfafjbjbgd

The article addresses an issue brought to light in previous work showing that the Schelling model of segregation displays a decreasing entropy trace link to paper. In order to produce a model consistent with fundamental physical paradigms a model improvement is made where a monetary variable extends the dynamics for urban mobility. The dual dynamic system shows a greater stability in the entropy trace supporting the idea that all complex systems adhere to the principles of physics.

A key concept is that as the movement patterns during the simulation iterations act to reduce the entropy, the monetary store of the agents is expended to their local enviornment to hypothetical costs increasing the entropy as a byproduct.

Example of the spatial arrangement of the agents on a grid

An analogue of the spatial label organization on the grid is made for income values of the agents

The sampled density of the microstate space considering the homogeneity values for the grid and that of the monetary variable

Entropy trace of the dual dynamic Schelling model

The income distribution used is derived from the USA social security report