A Spanish mathematician has created
a mathematical model of how marriages and relationships break down. Termed "sentimental dynamics", José-Manuel Rey's theory is based on the second law of thermodynamics, and posits an optimum amount of "energy" which needs to be fed into a relationship to sustain 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. The policy can break down if there is a tendency to reduce the effort because maintaining it causes discomfort, or because a lower degree of effort results in instability. Paradoxically, according to the second law model, a union everyone hopes will last forever is likely break up, a feature Rey calls the “failure paradox”.
The paper may be found
here. (Aside: note the use of the Unicode ♥ character in the equations; I wonder how common unusual Unicode symbols are in mathematical or scientific papers these days.)