Spanish mathematician Jose-Manuel Rey has calculated the "second thermodynamic law for sentimental interaction" and charted the trajectory of "sentimental equilibrium." Just like a relationship that is falling apart, it is as complicated as it is inscrutable.
Here's how PhysOrg explains Rey's law for sentimental interaction:
Using the optimal control theory model, Rey developed an equation based on the "second thermodynamic law for sentimental interaction," which states a relationship will disintegrate unless "energy" (effort) is fed into it.
The results of the mathematical analysis showed when both members of union are similar emotionally they have an "optimal effort policy," which results in a happy, long-lasting relationship.
As for that chart,
Breakup mechanics. The model produces a plausible scenario, through a sequence of effort inattentions, for the deterioration of a relationship in a gradual form, which seems to be typical according to data. Because of the effort gap, there is a tendency to lower the right effort level. Then the intrinsic instability of sentimental dynamics obeying the second law causes the piecewise decaying trajectories to move further and further away from the target trajectory and eventually to cross the threshold level xmin. This is considered a point of pre-rupture, since it is a matter of time before effort is abandoned.