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I've recently been imagining a world of magic with heavy influence from chinese wuxia and xianxia. In such worlds, there's often various fire and ice magic, among other different types. Now, fire magic is easy as there's seemingly no limit to the amount of heat/energy a certain substance can contain. Ice, however, is simply the lack of heat and has a hard cap of absolute zero, which in a world of infinitely powerful beings is quite insignificant. After all, a being that could produce fire of several thousand degrees easily wouldn't really be bothered by a mere -270 degrees.

Is there any way to make ice magic work, bringing it to negative degrees in the range of thousands, while still having it follow the laws of physics, even if loosely?

One handwave you could use would be to give ice magic the ability to magically increase the specific heat of an object while it is chilled. The result would be that the iced object would act like a thermal reservoir. A hot object with a reasonable normal specific heat could naturally get as hot as expected, glowing hot if needed, but would have a similar heat capacity to a cold object which had a supernaturally increased specific heat.

It would still have to chill the environment slowly, because it's temperature would still not be able to go below 0K, but it would be able to chill much more massive objects because it would be a huge cold reservoir, due to its artificially high specific heat.

Then it's up to you and your magic system to explain why fire mages do not have a similar capability, but that's another question.

The measure of a cold magician is not really how low they can bring the temperature. As you say there's a hard limit. They call it "absolute" zero for a reason. The real measure of a cold magician is "how much heat can they absorb?". If they can absorb more calories of heat than Fire-guy can generate then they win regardless of how cold they can make things. In the end all they need is "cold enough to keep themselves from being burned and cold enough over there to freeze their opponent".

Is there any way to make ice magic work, bringing it to negative degrees in the range of thousands, while still having it follow the laws of physics, even if loosely?

Well, no. According to the kinetic model, at any temperature corresponds a certain velocity of the molecules in any substance. At the temperature of 0 K the molecules are still. Once they are still they cannot get more still. Thus it's meaningless to talk about negative absolute temperatures.

After all, a being that could produce fire of several thousand degrees easily wouldn't really be bothered by a mere -270 degrees.

That's not exactly true. As said before, at 0 K molecules are perfectly still. According to Heisenberg indetermination principle, one cannot known both position and velocity of a molecule with arbitrarily high accuracy.

If you skew a bit the interpretation of this principle, since you know the velocity with perfect accuracy (you know they are still), you know nothing about their position, that is the thing at 0 K ceases to have a given position and could be everywhere.

You could view ice/fire magic as a means of transferring energy, and cap the rate at which energy can be transferred. Changing the temperature of 1kg of material X by 10 degrees will result in the same magnitude of energy change, whether that change is positive or negative. An ice mage could lower the temperature of an object by 100 degrees, but if a fire mage wants to raise the temperature by 1000 degrees, he needs to be 10 times as powerful.

One issue is that this nerfs the fire mage side of things, as an ice mage could hit absolute zero, while an equally-powered fire mage couldn't even start a campfire in the same amount of time. Maybe fire mages are generally more powerful, or maybe there's some conversion factor that heating an object requires only half the magical energy as cooling it, or perhaps it just takes fire mages longer to cast their inferno spells. I don't see any way for ice mages to hit temperatures below absolute zero without ignoring physical principles.

The fire mage is adding heat energy. The ice mage is substracting heat energy. Once the ice mage has subtracted all the heat energy he cant go lower... But he could try to do alternative things.

1: the ice mage adds potential negative energy. A fire mage (or just the outside world heating it up) requires more energy to get it from zero Kelvin to 1 degree higher than it would normally take.

2: after sucking all the heat energy out he'll start sucking potential energy. First the potential energy of say a fire mage who heats things up, then potential chemical energy, like the energy used to activate muscles or send nerve impulses...

3: why would the cap of absolute zero be less dangerous than heating something to thousands of degrees? We know that the colder things get, the weirder things get as well. Superfluids anyone? Or other effects? https://www.google.com/amp/s/phys.org/news/2015-06-absolute-molecules-exotic-states.amp