Formula del amor

A Mathematical Model of Sentimental Dynamics Accounting for Marital Dissolution
´ Jose-Manuel Rey*
´ ´ Departamento de Analisis Economico, Universidad Complutense, Madrid, Spain

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 theexistence 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 emotionalattributes, 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 mathematicalfacts 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.
Citation: Rey J-M (2010) A Mathematical Model of Sentimental Dynamics Accounting for Marital Dissolution. PLoSONE 5(3): e9881. doi:10.1371/ journal.pone.0009881 Editor: Jeremy Miles, RAND Corporation, United States of America Received September 17, 2009; Accepted February 14, 2010; Published March 31, 2010 ´-Manuel Rey. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits Copyright: ß 2010 Jose unrestricted use, distribution, andreproduction in any medium, provided the original author and source are credited. ´ Funding: This work was partially supported by Ministerio de Ciencia e Innovacion (Spain) through MTM2006-02372 and MTM2009-12672. The funders had no role in research design, decision to publish, or preparation of the manuscript. Competing Interests: The author has declared that no competing interests exist. * E-mail:j-man@ccee.ucm.es

Introduction
Sentimental relationships of a romantic nature are typically considered a fundamental component of a balanced happy life in western societies [1]. When people are asked what they believe necessary for happiness they usually give priority to ‘love’ or to ‘a close relationship’ [2], [3], [4]. It is hard to think of another aspect of human life involving so many cultural,sociological, psychological or economic issues. Whereas the initial stage of romantic relationships seems to be controlled by chemical processes (see [5] and references therein), the issue of maintaining a sentimental relationship may rather belong in the realm of rational decisions. People usually engage in long-term relationships –typically marriage– only after due consideration. Even in theprevalent western scenario of sequential monogamy, couples generally assert their intention to make their relationship last and be happy together (see data reported in section 2). But the high divorce rates massively reported across Europe and in the United States show a resounding failure in their program implementation. The phenomenon of couple disruption is considered epidemic in the US where thestatistic ‘one in two couples end in divorce’ is quoted repeatedly in the media and in academic reports. The average rate in EU27 is not far below that figure and some countries in Europe show higher rates of divorce. Furthermore, data on unmarried couples tell an even worse tale of sentimental break ups (see section 2.) There is general agreement among scholars from different fields on mainly...