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Examining the Schelling Model Simulation through an Estimation of Its Entropy
Alexander V Mantzaris1, John A Marich1, Tristin W Halfman1
1Department of Statistics, University of Central Florida (UCF), TC2 4000 Central Florida Blvd, Orlando, FL 32816-2370, USA.
Entropy (Basel, Switzerland)
|December 3, 2020
Summary
The Schelling model shows that initial random resident placements have higher entropy than segregated states. As homogeneity increases, the system
Area of Science:
- Statistical mechanics
- Computational social science
- Agent-based modeling
Background:
- The Schelling model describes residential dynamics based on neighbor similarity.
- Previous research linked it to the Ising model due to local dependency.
- Statistical mechanics concepts are applicable to segregation models.
Purpose of the Study:
- To develop a methodology for estimating entropy in the Schelling model.
- To quantify entropy across different simulation states.
- To analyze entropy changes during segregation dynamics.
Main Methods:
- Utilized a Monte Carlo estimation approach.
- Defined macrostates by aggregate homogeneity satisfaction.
- Traced estimated entropy values per lattice configuration state.
Main Results:
- Initial random configurations exhibited higher entropy.
- Final segregated states showed lower entropy.
- Entropy decreased as residential homogeneity increased.
Conclusions:
- The Schelling model's entropy is state-dependent.
- Segregation dynamics lead to decreased system entropy.
- This provides a quantitative measure of disorder in segregation patterns.
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