Static magnetism likely begins when two magnets are brought close to one another. Max's equations coupled with Lorentz' laws will push ions in a circular fashion. Torqued ions if you will. The electrons will move radically faster than their slower, more massive nuclei. The evacuation of electrons will cause a counter pull of electrons back towards the 'positively' charged ions that remain.
Eventually all ions will have moved out and the evacuated space in the center will cause the 'North' end of the magnet to be pulled towards the 'South' end. Next we hear "click".
Now we need a model. The Massachusetts Institute of Technology and Queen's University in Kingston Ontario would prefer a discrete stochastics model to deal with the movement and relative charge-mass of these particles.
The Poisson arrivals relative to another particle with a relatively different set of Poisson parameters gives rise to what can be modeled as the binomial distribution. We move quickly to Gauss' famous distribution because we love to deal in the continuous charge-mass domain.
The arrivals would actually be departures in this case. Similar to the concept of stochastic gravity the evacuating electrons, as a ratio of charge-mass, to the remaining nuclei. Differential equations can then be used to show a net dmass/dt from the region between the 'North' and 'South' sides of the magnets.
Electron flux in what is known as a curl in the field in calculus is central to this concept.
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