Version 1
: Received: 16 July 2018 / Approved: 17 July 2018 / Online: 17 July 2018 (11:57:36 CEST)
Version 2
: Received: 21 August 2018 / Approved: 22 August 2018 / Online: 22 August 2018 (11:21:05 CEST)
Mantzaris, A.V.; Marich, J.A.; Halfman, T.W. Examining the Schelling Model Simulation through an Estimation of Its Entropy. Entropy2018, 20, 623.
Mantzaris, A.V.; Marich, J.A.; Halfman, T.W. Examining the Schelling Model Simulation through an Estimation of Its Entropy. Entropy 2018, 20, 623.
Mantzaris, A.V.; Marich, J.A.; Halfman, T.W. Examining the Schelling Model Simulation through an Estimation of Its Entropy. Entropy2018, 20, 623.
Mantzaris, A.V.; Marich, J.A.; Halfman, T.W. Examining the Schelling Model Simulation through an Estimation of Its Entropy. Entropy 2018, 20, 623.
Abstract
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.
Keywords
Schelling Model; Spatial Analysis; Entropy
Subject
Physical Sciences, Mathematical Physics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
