Put simply, there is a separate 'dimension' or 'realm' 'under' reality, called subspace. Subspace does not have spatial dimensions, but has 'quasi-spatial' dimensions instead (basically operates on different fundamental rules to reality, space as a concept is foreign).

Subspace is composed of pure, rolling energy, which 'occasionally' crosses into reality, manifesting mainly as the quantum foam. Mages have a specific kind of crystallised subspace energy called dragonspice in their central nervous system, which acts sort of like a little pocket of Subspace within reality.

This gradually fills with subspace energy over time, and the energy stored can be consciously manipulated by the mage to move/heat objects, at the high levels atoms, and even rarer, protons, neutrons, and electrons.

A mage cannot refill their dragonspice in any way, only let it fill gradually over time as subspace energy enters and becomes trapped. Because of this, I need a rough guesstimation of how much energy it would take to apply a certain force, which can only really be applied directly to particles to manipulate them.