Not strictly mathematical but,
Magnetic Fields, B and H, store energy..
E = 1/2 B x H
Apparently it is a 'cross' product.
I might assume, or guess, that if the fields were not 'closed' then the energy would 'leak' away of its own accord.
You do get 'losses' but that would be the energy being 'coupled' to a loss mechanism, resistive, either in the conductors or magnetic materials being used, or anything influenced by such fields with similar 'loss' mechanisms.
Genome.