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A Mathematical Model of Sentimental Dynamics Accounting for Marital Dissolution

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  • José-Manuel Rey

Abstract

Background: Marital dissolution is ubiquitous in western societies. It poses major scientific and sociological problems both in theoretical and therapeutic terms. Scholars and therapists agree on the existence of a sort of second law of thermodynamics for sentimental relationships. Effort is required to sustain them. Love is not enough. Methodology/Principal Findings: Building on a simple version of the second law we use optimal control theory as a novel approach to model sentimental dynamics. Our analysis is consistent with sociological data. We show that, when both partners have similar emotional attributes, there is an optimal effort policy yielding a durable happy union. This policy is prey to structural destabilization resulting from a combination of two factors: there is an effort gap because the optimal policy always entails discomfort and there is a tendency to lower effort to non-sustaining levels due to the instability of the dynamics. Conclusions/Significance: These mathematical facts implied by the model unveil an underlying mechanism that may explain couple disruption in real scenarios. Within this framework the apparent paradox that a union consistently planned to last forever will probably break up is explained as a mechanistic consequence of the second law.

Suggested Citation

  • José-Manuel Rey, 2010. "A Mathematical Model of Sentimental Dynamics Accounting for Marital Dissolution," PLOS ONE, Public Library of Science, vol. 5(3), pages 1-8, March.
  • Handle: RePEc:plo:pone00:0009881
    DOI: 10.1371/journal.pone.0009881
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    References listed on IDEAS

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    Cited by:

    1. Dario Bauso & Ben Mansour Dia & Boualem Djehiche & Hamidou Tembine & Raul Tempone, 2014. "Mean-Field Games for Marriage," PLOS ONE, Public Library of Science, vol. 9(5), pages 1-15, May.
    2. Jorge Herrera de la Cruz & José-Manuel Rey, 2021. "Controlling forever love," PLOS ONE, Public Library of Science, vol. 16(12), pages 1-21, December.
    3. Pei, Xin & Zhan, Xiu-Xiu & Jin, Zhen, 2017. "Application of pair approximation method to modeling and analysis of a marriage network," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 280-293.
    4. Rinaldi, Sergio & Della Rossa, Fabio & Landi, Pietro, 2013. "A mathematical model of “Gone with the Wind”," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(15), pages 3231-3239.

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