The nowadays love’s crisis
Nearly few thousand of scientific articles each year have been written about emotion. The number has grown exponentially in the last thirty years; growth has also occurred in related areas, contributing to a better understanding of the nature and neurobiological mechanisms implicated in emotions. These findings offered a new perspective from which to treat illnesses involving emotional disorders. Love is a complex mental function, which has been found to interact with other mental functions, such as memory, attention, perception such as taste, and reasoning; it even has been shown to affect health. When people are asked what they believe necessary for happiness they usually give priority to ‘love’ or to ‘a close relationship’. 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. Couples generally assert their intention to make their relationship last and be happy together. 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, furthermore, data on unmarried couples tell an even worse tale of sentimental break ups. Marital instability has a devastating effect on our society. In general, marital disruption results in negative physical and psychological health outcomes, involving consequences for children, adolescents and adults. This is a theme of paramount importance in the social sciences since marriage is considered a “cultural universal” and the fundamental social institution of most societies in world history.
Also, marriage has significant implications on health and well-being. It has been consistently documented that high quality social relationships, particularly a functional marriage, have protective effects on the mental and emotional health of individuals.
A successful relationship needs efforts when the feeling decline: the thermodynamics second law explains it’s impossible to transfert heat without energy from the outside
Many studies have started considering long-term successful marital relationship under a mathematical point of view. A recent study put the attention on simulations of the state (or quality) of the relationship. This state can be monitored by a time variable x(t) – called the feeling here – whose evolution is controlled by the couple through the effort each partner puts into the relationship. Taking into account Sternberg’s triangular theory of love based on the three points which engage live, that are passion, intimacy and commitment, x(t) can be thought to be related with the non-rational dimensions of love, passion and intimacy, while c1(t) and c2(t) may represent the rational dimension decision/commitment. Dynamical systems theory provides a suitable toolbox for modeling the temporal evolution of a dyadic system. A romantic relationship can be considered a dyadic system.
Building and sustaining a high-quality marriage requires a deliberate effort, but how much effort? The answer is in the trajectories of the variables c1(t) and c2(t) for a successful relationship. The effort paths are determined for the couple to obtain maximal happiness. Essentially, there are two perspectives to describe the trajectory of a successful relationship: after a continuous decline, either stabilization of marital quality follows (stability perspective) or a small upturn of marital quality occurs (resilience perspective). Our results suggest that both the stability and the resilience perspectives can occur for successful trajectories.
While successful relationships with no exogenous stress show the stabilization pattern, those undergoing some episode of stress may exhibit a U-shaped feeling curve. Regarding the effort question, we find evidence that effort trajectories must increase until reaching a plateau as the feeling stabilizes.

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But how act these trajectories? Following the differential love games, successful trajectories depend on the cognitive processing of emotional rewards and costs for both partners in the relationship. The initial feeling x(0) = x0 is typically very large. The feeling obeys the second law of the thermodynamics for sentimental relationships: there is a natural tendency of x (t) to decay in time, which can be counteracted with the effort made by both partners. The evolution law is a differential equation that can be considered as the state equation for the effort control problem of the couple. The complex solutions of the equation lead to these findings.
Maintaining a rewarding relationship is always costly in terms of effort
Sustaining a happy relationship requires an extra effort higher than the favorite level calculated. successful couples must expect a continuous decline of relationship quality until a plateau is eventually reached. This pattern is in accord with the stability perspective of marriage. Marriages that end in divorce are expected to show a steady and uninterrupted decline in marital quality until they finally break up. Successful couples must increase their effort over time as marital quality declines, until both feeling and effort eventually approach constant levels. As mentioned above, a successful effort trajectory lies above the favorite level. Maintaining a rewarding relationship is always costly in terms of effort: no matter how much effort a partner is willing to put in, the required effort is more demanding.
Couples committed to thriving in the long term are probably aware that they will be facing certain stressful life events –some of them unpredictable. Our analysis suggests that they should be prepared for a noticeable impact on the quality of their relationship and go the extra mile for some time to bring the relationship, slowly, back to the pre-crisis level. On the other hand, the feedback analysis shows that, for successful marriages overcoming stressful periods, marital quality exhibits a U-shape pattern over time, as it is shown in figure. This result is consistent with the marital resilience perspective for marriages that avoid divorce.
Successful couples who overcome stressful life events show a curvilinear feeling trajectory due to a relative increase in happiness in a later period. This pattern is observed in resilient relationships that implement a feedback stabilization mechanism. Such U-shaped trajectories are consistent with the marital resilience perspective which relies on explanations based on changes in family roles and structures.
References:
https://doi.org/10.1371/journal.pone.0260529