The Math of Breaking Up

From PhysOrg.com: Most people know love takes work, and effort is needed to sustain a happy relationship over the long term, but now a mathematician in Spain has for the first time explained it mathematically by developing a dynamical mathematical model based on the second law of thermodynamics to model "sentimental dynamics." The results are consistent with sociological data on marriage breakdowns.



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.