In designing a hard magic system, I would like to keep things consistent with the laws of thermodynamics (as many do) since, if I don't, I fear I may accidentally create a way for mages to create infinite energy. Also because our intuitions about how energy work are, whether or not people realise, heavily based on these laws. They're fairly intuitive since we live in a world where their effects are constantly observable.
I imagined a system where there is some 'Aether' field from which a mage draws energy. They have some personal 'stock' which is spent when they cast a spell. There is a standard energy conversion: 'magical' into 'physical (whether that be thermal, kinetic, electrical etc...) Standard stuff. Originally, I was planning on having the mages power regenerate over time. They just kind of absorb this energy to refill their 'stock' over time.
However, this energy is itself analogous to thermal energy. When talking thermodynamics, the 2nd law states that energy cannot spontaneously flow from a cool body to a hotter body. So, using the analogy between this magical energy and thermal energy (both are a scalar field), the mage would at some point be a hotter body and therefore no more energy would flow into them.
I suppose I could fix this by saying that the mage's energy reaches an equilibrium with the rest of the magic energy field. As far as I can tell, this would solve the problem but I wanted more experienced mages to have a larger 'stock' than their less experienced peers.
The main questions:
Are there any other similar solutions to this problem? How can mages fill up on energy from some magical source that doesn't break these rules?
Am I mistaken in saying that my system breaks thermodynamics?
By the way, I have studied a bit of physics and mathematics. I'm not too scared of equations.