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

Abstract

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.

Exploring the entropic nature of political polarization through its formulation as a isolated thermodynamic system

“…www.nature.com/scientificreports/ lower value. This is something that is to be expected in an isolated system with rules aiming towards achieving homogeneity 38 , and comes into agreement with previous studies investigating the Schelling model such as in 20,23 . This does not reflect a realistic physical system that would inevitably be expected to respect the second law of thermodynamics as S I,t should be increasing.…”

“…Model definitions for the political engagement model with time constrained agent actions. Although there are potentially many variables to consider as candidates to incorporate into the model to address the decreasing entropy trend, such as a monetary variable 23 , it is proposed here that an even more fundamental aspect of the agents can be considered and that is their limited time as a resource. That their time will be shared among other activities outside of the political discourse, and assuming that the amount of time spent in activities is constant; this allows a constraint to be applied.…”

“…That their time will be shared among other activities outside of the political discourse, and assuming that the amount of time spent in activities is constant; this allows a constraint to be applied. Introducing a constraint between variables provides an intrinsic coupling between variables that can change the state space rather than have associated independent dynamics which are plausibly coupled (such as residential movements and financial expenditure 23,24,34 ).…”

“…In the work of 20 the Schelling model of segregation 21,22 has its entropy trace along the simulation produced showing a decrease with the increased agent homogeneity, and in 23 it is shown how with a dual dynamic operating on an income variable that the overall extended Schelling system can display an increasing entropy trace and respect the second law of thermodynamics. The motivation for the inclusion of a monetary variable as influencing the residential movements was inspiration from the work of 24 that observed this from real world data collected.…”

“…In 23 the extension to the Schelling model has a monetary dynamic associated with every move an agent makes on the grid that affects an income variable. This variable and dynamic does have the effect where the overall system entropy can be seen to increase due to the identity entropy decrease that is matched and overcome by the increase in the monetary entropy component.…”