José Manuel Rey Simó, from the Departamento de Análisis Económico, Universidad Complutense, Madrid, Spain, explains his ESSAY "A Mathematical Model of Sentimental Dynamics Accounting for Marital Dissolution"
The second law of thermodynamics, postulates that entropy (randomness) increases over time in a system that is not in equilibrium.
Rey explains about relationships:
1)"Effort is required to sustain them. Love is not enough"
2)"There is an epidemic failure in love relationships"
3) "Couples typically conceive a relationship that lasts to be the main element in their pursuit of happiness. Moreover, most of them think that their own relationship will not collapse"
4) "Couple disruption is the outcome of a gradual deterioration process"
5) "The subjective well-being of partners decreases after marriage"
The application of entropy to relationships was based on 3 assumptions:
1) "(Weak Homogamy) Both partners share the same traits according to the model specifications below. Equivalently, the couple is the decision unit for the planning problem"
2) "(Second law of thermodynamics for sentimental relationships) There is tendency for the initial feeling for one another to fade away. This kind of inertia must be counteracted by conscious practices"
3) "(Utility structure) There are two independent sources of utility. One comes from the level of feeling of attachment and the other is the consequence of the intensity of effort."
Whereas the initial stage of romantic relationships seems to be controlled by chemical processes, the issue of maintaining a sentimental relationship may rather belong in the realm of rational decisions.... 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 the statistic
'one in two couples end in divorce' is quoted repeatedly in the media and in academic reports.
Furthermore, data on unmarried couples tell an even worse tale of sentimental break ups.
Indeed, it is not understood at this juncture why so many couples end in divorce while some others do not.
Building on sociological data, we propose a mathematical model based on optimal control theory
accounting for the rational planning by a homogamous couple of a long term relationship.
I had sent to Dr. Rey Simó a collection of papers about personality similarity.
Klohnen & Mendelsohn in 1998
"romantic partners showing strong similarity in age, political, and religious attitudes; moderate similarity in education, general intelligence, and values; and little or no similarity in personality characteristics "
Klohnen & Luo in 2005
"ASSORTATIVE MATING AND MARITAL QUALITY IN NEWLYWEDS: A COUPLE CENTERED APPROACH", February 2005 at "Journal of Personality and Social Psychology"
Page #19 of PDF whitepaper
Page #322 of magazine
Couple Similarity and Marital Quality
Our study presents one of the most comprehensive examinations of the similarity-satisfaction link. The observed SIMILARITY-SATISFACTION CORRELATIONS SUGGEST THAT SIMILARITY ON PERSONALITY RELATED DOMAINS WAS STRONGLY ASSOCIATED WITH SATISFACTION, whereas similarity on attitude-related domains was not.
People may be attracted to those who have similar attitudes, values, and beliefs and even marry them (at least in part) on the basis of this similarity. However, once individuals are in a committed relationship, IT MAY BE PRIMARILY PERSONALITY SIMILARITY THAT INFLUENCES MARITAL HAPPINESS. This suggests that attitude and value similarity may play a different role in relationship development than personality similarity does. For example, whereas similarity in attitudes and values appears to be important early on in the relationship and may play an important role in relationship progression, personality similarity becomes more important as the relationship reaches greater commitment. Our empirical findings and this proposition are certainly consistent with "filter" or "process" theories of relationship development (e.g., Kerckhoff & Davis, 1962; Murstein, 1980) that hold that patterns of similarity and complementarity on different individual-difference domains play differential roles at different points in the relationship development process.
……………. FUTURE RESEARCH designed to better understand these underlying processes is needed.