We already know that long-lasting relationships aren’t powered by love alone—they require continuous “energy” and effort, especially during difficult periods. Psychologist John Gottman has compared relationships to a closed system: without added input, they naturally decline over time.
A mathematical approach using dynamic systems models relationship “love” as a variable that changes based on partners’ ongoing effort. The key insight is that stable couples increase effort when destabilizing events occur (stress, conflict, life crises), and sometimes the more emotionally invested partner must temporarily carry more of that load. The model also suggests relationships with larger background differences (cultural, economic, religious, social) may face higher long-term strain if effort becomes chronically imbalanced. The takeaway: lasting relationships rely on deliberate maintenance, fair repair after conflict, and adaptive teamwork—not just strong feelings.
For years, science has
been trying to understand why love ends and what are the mechanisms that lead
to the end of a relationship.
Researchers have managed
to find a mathematical law that explains how a long-lasting relationship works:
it is possible, but love is not enough.
Science has finally
revealed the secret of happy relationships into old age. After years of study,
a group of researchers managed to create a mathematical model that describes
exactly how a successful couple's relationship works.
In several Western
countries, 50% of couples do not "live" more than 25 years. The truth
is, by their very nature, relationships tend to end and couples tend to break
up.
Now, some researchers
have pieced together the information processed so far to discover the laws
behind those few couples who seem to avoid this inevitable fate.
Relationships also have
their own laws: Who works harder for eternal love?
As an extensive article
published in The Conversation explains, a relationship works more or less like
what is called a closed system. The first to state this was the psychologist
John Gottman, according to which the relationship between two partners essentially
obeys the second law of thermodynamics. In short, a closed system is exhausted
if it is not supplied with energy: basically, it is not enough for a
relationship to last if nothing is done to improve it.
A study led by the
University of Madrid tried to verify whether or not this law was confirmed by
applying dynamic systems, that is, those mathematical tools used to study the
evolution of a variable over time.
In this case, the
variable is the feeling of love in the couple, which, according to Gottman's
theory, is affected by the energy that the members of the couple give off. The
authors of the study talk about the partners' "effort" to make the
feeling last forever. These models showed that in order to achieve its purpose,
the relationship requires a level of effort on the part of the partners that
exceeds what they would be inclined to It is precisely this difference between
the natural effort and the necessary effort that endangers the stability of the
couple and risks ultimately causing the end.
The love equation
unraveled: Researchers have cracked the key to long-lasting relationships.
It seems love doesn't pay
any attention to the laws of karma. The mathematical model showed that, in
functioning couples, when an external destabilizing factor arises - a problem
or a crisis - both partners must increase their level of effort to overcome it,
but the one who is more emotionally involved at the time it is he who must make
a greater effort.
This difference in effort
can also occur in so-called heterogamous couples, that is, those in which there
is a difference in environment (social, religious, cultural or economic)
between the two partners. Indeed, it appears that homogamous relationships,
meaning relationships where the members come from very similar backgrounds, are
generally more stable and more likely to last. In these cases, the differences
between the two people may actually cause them to put a different amount of
effort into the relationship, but this asymmetry can become destructive to the
couple in the long run.


