The correlation between dragons and magic does NOT imply causality-
'Magic' has anecdotally grown in efficacy circa their apparent arrival...
But to conclude that dragons generate it rather than simply herald or portend the waxing of 'magical energy' would be erroneous and a reductive fallacy.
Please recall that the white walkers were the first 'magical' or mythical creatures to reappear in this saga-
Followed by ominous portents and a reawakening of 'magical powers' in the stark family blood(of the first men) line
Then finally the red comet and dragons-
The dragons are merely the most notable landmark on the recent timeline of events that the fallible third person POV would associate to current changes in the metaphysical dynamics of their lives....
As stated by melisandre and the pyromancers, etc.
The name of the saga is " a song of fire and ice " draw your own conclusions about the metaphysical nature of magic in this mythos as it may relate to duality and polar changes of state within the same continuum...
But since the word 'physic' is the root of metaphysic perhaps doing a simple wiki read on physical nature of fire and it's typical chemical constituency might help??? (As would actually reading the books-)
One eyebrow quietly raised? I'll give you a hint .
Fire and water are made of, and require the exact same stuff, as well as products of each other.
fuel and oxidizer. Diametric DUALITY of nature?
Seems rather like particle physics and physical chemistry in our "non-magical world", doesn't it? Think charged and relaxed atomic states, binary data, two magnetic poles making one continuum field---
You may also recall that it has been said more than once that it isn't known whether 'the white walkers bring the winter or it brings them, but the two are connected'
Coincidentally white walkers being made of ice (a crystal with inherent harmonic resonance) can be shattered by obsidian in much the same way as glass can by ceramic.
Realizing that the seasons are incalculable and erratic, you might deduce this planet to be in a binary star system...
Physics and cosmology-
If this isn't coming together for you I'll just spell it out-
The "metaphysics" and physics of 'magic' in the world of fire and ice is a literary metaphorical trope for the paradoxical nature of dualities and continuums in our own world, and the way in which many seemingly unrelated or distantly related systems of organization are actually codependent or interdependent in a synergistic way influencing state changes in one another-