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Examining the Schelling Model Simulation through an Estimation of Its Entropy
The Schelling model of segregation allows for a general description of residential movements in an environment modeled by a lattice. The key factor is that occupants change positions until they are surrounded by a designated minimum number of similarly labeled residents. An analogy to the Ising mode...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2018
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7513139/ https://www.ncbi.nlm.nih.gov/pubmed/33265712 http://dx.doi.org/10.3390/e20090623 |
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author | Mantzaris, Alexander V. Marich, John A. Halfman, Tristin W. |
author_facet | Mantzaris, Alexander V. Marich, John A. Halfman, Tristin W. |
author_sort | Mantzaris, Alexander V. |
collection | PubMed |
description | The Schelling model of segregation allows for a general description of residential movements in an environment modeled by a lattice. The key factor is that occupants change positions until they are surrounded by a designated minimum number of similarly labeled residents. An analogy to the Ising model has been made in previous research, primarily due the assumption of state changes being dependent upon the adjacent cell positions. This allows for concepts produced in statistical mechanics to be applied to the Schelling model. Here is presented a methodology to estimate the entropy of the model for different states of the simulation. A Monte Carlo estimate is obtained for the set of macrostates defined as the different aggregate homogeneity satisfaction values across all residents, which allows for the entropy value to be produced for each state. This produces a trace of the estimated entropy value for the states of the lattice configurations to be displayed with each iteration. The results show that the initial random placements of residents have larger entropy values than the final states of the simulation when the overall homogeneity of the residential locality is increased. |
format | Online Article Text |
id | pubmed-7513139 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2018 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-75131392020-11-09 Examining the Schelling Model Simulation through an Estimation of Its Entropy Mantzaris, Alexander V. Marich, John A. Halfman, Tristin W. Entropy (Basel) Article The Schelling model of segregation allows for a general description of residential movements in an environment modeled by a lattice. The key factor is that occupants change positions until they are surrounded by a designated minimum number of similarly labeled residents. An analogy to the Ising model has been made in previous research, primarily due the assumption of state changes being dependent upon the adjacent cell positions. This allows for concepts produced in statistical mechanics to be applied to the Schelling model. Here is presented a methodology to estimate the entropy of the model for different states of the simulation. A Monte Carlo estimate is obtained for the set of macrostates defined as the different aggregate homogeneity satisfaction values across all residents, which allows for the entropy value to be produced for each state. This produces a trace of the estimated entropy value for the states of the lattice configurations to be displayed with each iteration. The results show that the initial random placements of residents have larger entropy values than the final states of the simulation when the overall homogeneity of the residential locality is increased. MDPI 2018-08-21 /pmc/articles/PMC7513139/ /pubmed/33265712 http://dx.doi.org/10.3390/e20090623 Text en © 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Mantzaris, Alexander V. Marich, John A. Halfman, Tristin W. Examining the Schelling Model Simulation through an Estimation of Its Entropy |
title | Examining the Schelling Model Simulation through an Estimation of Its Entropy |
title_full | Examining the Schelling Model Simulation through an Estimation of Its Entropy |
title_fullStr | Examining the Schelling Model Simulation through an Estimation of Its Entropy |
title_full_unstemmed | Examining the Schelling Model Simulation through an Estimation of Its Entropy |
title_short | Examining the Schelling Model Simulation through an Estimation of Its Entropy |
title_sort | examining the schelling model simulation through an estimation of its entropy |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7513139/ https://www.ncbi.nlm.nih.gov/pubmed/33265712 http://dx.doi.org/10.3390/e20090623 |
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