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(Note: this is similar to is Cryomancy scientifically possible?, but not exactly the same.)

In my story, I have "magic" that amounts to telekinesis powered by the user's metabolism.

It seems that heating objects using this magic should be pretty plausible (although the amount of heat that can be generated is somewhat limited); the user metabolizes some energy, and that energy, instead of doing Work inside the user's body, causes a target object to heat up by that amount of energy. More specifically, the way I envision this working is something like the user's body produces energy via metabolism as normal ("using magic" can be though of as an additional way to trigger metabolic energy production), but the energy produced is magically teleported to a location of the user's choice and acts in a direction of the user's choice. (I think this is sufficient to blur the lines between "heat" energy and other, more useful forms of kinetic energy, thus explaining why a magic user can also do things like levitate small objects. This is playing pretty fast-and-loose with entropy, but it is magic, although the difference in entropy may factor in as a loss in efficiency.) There is also a range limit, with "lost" energy dissipating as heat between the magic user and the target. (Basically, at a distance $D$ from the target, the magic user must spend $2x$ energy to apply $x$ to the target, with the other $x$ getting lost somewhere en route, possibly as infrared radiation.)

To phrase this a little differently... magic is a lot like a combination of Newton's Cradle — a moving ball strikes a stationary mass in an inelastic collision, and the energy is transferred through the mass (without the stationary mass moving itself) to another ball — and a "super ball" — an object which, upon striking an "immovable" object, rebounds in a perfectly elastic collision such that its speed remains constant but the direction of its motion changes. All (my story's) magic brings to the party is that these effects are combined, i.e. it is like a Newton's Cradle where the stationary mass is immaterial (and can transfer energy/force through other matter occupying the same space as the immaterial "mass" with minimal effect on said matter), and can redirect the force in a different direction. (Propagation is presumably still subject to the speed of light, but for my purposes this is effectively negligible; magic only works over short distances.)

Now... it also seems like the reverse of heating things should be possible. After all, cooling is just applying an acceleration to atoms in opposition to those atoms' present velocity, and we certainly have technological means of cooling things (note the referenced question and answers thereto).

The problem is that this appears to violate thermodynamics; we can't just decrease the entropy of the universe. In particular, the "naïve" solution would be to postulate that the metabolic energy produced by the magic user perfectly counteracts the existing atomic motion of the target to be cooled, but this implies that the user's metabolism produces $k$ energy which doesn't just not affect the user directly, but effectively vanishes from the target. IOW, I just removed $2k$ energy from the universe (and incarnated Maxwell's Demon in the process).

How can I avoid violating thermodynamics in this manner, but still allow magic to cool things? I'm looking particularly for answers that can quantify how much heat needs to be dumped elsewhere (presumably into the magic user's body and/or surroundings).

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  • $\begingroup$ Isn't this just a different implementation of Maxwell's daemon? $\endgroup$ – L.Dutch - Reinstate Monica Jun 12 '20 at 17:30
  • $\begingroup$ @L.Dutch-ReinstateMonica, huh? I said in the question that it appears to be so. The question is how to avoid that. $\endgroup$ – Matthew Jun 12 '20 at 18:05
  • $\begingroup$ The beauty of quantum mechanic is that atoms only absorb specific energy level, keep stepping down the freq of light will slow "fast" atoms but won't affect "slow" one's... also terms and conditions apply ;D $\endgroup$ – user6760 Jun 12 '20 at 22:45
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You are basically asking for a heat pump. A lot of people learn that heat only flows from hot regions to cool regions. This is true, but isn't the whole story. You can make heat flow to a hotter region if you do work; this is what your refrigerator does.

The key to prevent this from violating the laws of thermodynamics is to make the telekinesis heat some reservoir more than it cools the target. Your refrigerator pumps the heat from inside to the rest of the room. This isn't 100% efficient either, so it also heats the room up a little extra. For example maybe it removes 1000 joules of heat from inside the fridge, but adds 1001 joules of heat to the rest of the kitchen.

You might still be violating other laws of physics, but this should be sufficient to not violate thermodynamics.

By the way, we actually do exactly what you're proposing in real life, but with lasers instead of magic.

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  • $\begingroup$ Yeah, I was reading about cooling lasers from the linked question 🙂. I guess what I'm asking is could a magic user expend "metabolic fuel" (probably a more correct term for this) to heat themselves by $x$ while decreasing the heat of something else by $x$? Or does that still violate conservation of energy, and actually they need to heat themselves by $2x$, or by some other amount? $\endgroup$ – Matthew Jun 12 '20 at 18:12
  • $\begingroup$ If they decrease the heat of something by x, they must increase the heat of themselves or some other reservoir by x+y, where y is some unavoidable inefficiency. You can minimize y, but never eliminate it entirely. $\endgroup$ – Ryan_L Jun 12 '20 at 18:50
  • $\begingroup$ ...but I have magic! Uh... I'm going to post my own attempt at an answer; fact-checking would be appreciated! $\endgroup$ – Matthew Jun 12 '20 at 19:07
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Without an established science on how telekinetic cooling works, we do not know how efficient it could be, but what we do know is refrigerators. According to https://physics.stackexchange.com/questions/230465/heat-rejected-by-a-refrigerator, a standard 25W refrigerator has an efficiency of about 17.4:1. Meaning one unit of energy is consumed for every 17.4 units of thermal energy you displace.

A good hard workout can typically burn up to 400 kCal; so, let's call this the cap on what you can safely do on a regular basis. This means that a common ice spell might displace somewhere around 29,140KJ of energy. It takes displacing about about 300KJ of energy to bring a gallon of water to freezing from room temperature; so, if your spell is as efficient as a refrigerator, you are looking at being able to freeze about 97 gallons of water with the same energy you would get from a light meal.

If you want to really go big, a lb of body fat contains about 3,500kCal of energy. A well fed cryomancer who just sits around all day playing video games and answering questions of stack-exchange might have a good 50lb of body fat he could tap into without emaciating himself. That would give him the power to create a 4" thick sheet of ice over an Olympic sized swimming pool turning the whole thing into a usable ice skating ring.

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  • $\begingroup$ One thing to consider is the power the telekinesis is capable of. Sure the person in your second example has 3,500kCal available, but how quickly can they spend it all? $\endgroup$ – Ryan_L Jun 12 '20 at 19:56
  • $\begingroup$ Yeah, the problem is that my magic system is based on having to "burn" $x$ via metabolism in order to dump $x$ (or less) into a system, and, well, it's based on telekinesis. Moving things, heating things, is easy. Directly opposing atomic vibration is plausible, but the magic user's own body must 'receive' the heat in such cases. Although this does make me wonder if I should just let "magic" work in reverse... $\endgroup$ – Matthew Jun 12 '20 at 20:09
  • $\begingroup$ @Matthew The caster does not need to be the heat sink, he could just turn the energy into radio waves and blast it off into space. $\endgroup$ – Nosajimiki Jun 12 '20 at 20:11
  • $\begingroup$ @Ryan_L Since there is no established science to telekinetic cooling, I'd say it could be whatever the author needs it to be, but if you need some scientific reference, working out burns a maximum of about 15kCal per minute. That should be enough to freeze about 3.6 gallons of water per minute. This is not a super impressive freezing speed, but still conceivably useful. $\endgroup$ – Nosajimiki Jun 12 '20 at 20:17
  • $\begingroup$ I think you are ignoring the mechanics I am trying to describe. Magic isn't free energy, nor does it allow moving energy from A to B for free. My initial premise is that a magic user can only "add" energy to a system by supplying that energy from his/her own metabolism. Some other mechanism is needed to "move" energy as you are describing. Plausibly, a magic user could compress a refrigerant into a container (let the container do the work of keeping it compressed!), wait for it to cool, then let it out. $\endgroup$ – Matthew Jun 12 '20 at 20:19
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Thought Experiment

Ryan_L inspired me to try a thought experiment that I think might help.

So far, I haven't been able to poke any gaping holes in heating something... a magic user produces $x$ energy from metabolic processes which, instead of performing Work (e.g. contracting muscles) or heating the user's body, instead dumps $x$ of heat energy into the environment (mostly, but not entirely, into some target). This seems okay, but if not, someone please jump in and yell at me.

Okay, how about cooling? The thought experiment that made me realize I definitely have a problem is this: let's say that, instead of trying to cool some target, the magic user tries to cool herself¹. Let's start by theorizing that this works in the manner of a perfectly efficient heat pump.

So, our hypothetical magic user produces (via metabolic processes) $x$ energy, which she uses to cool herself. Because that energy has to go somewhere, she dumps it also inter her own body... for a net change of zero.

However, there's a hitch. Her body temperature didn't change, but she did burn of some "biofuel"... and this energy just disappeared. This would be like lighting a bunch of gasoline, and seeing it undergo the usual chemical changes of combustion, but without giving off any heat.

Clearly, this won't work.

More Rambling

Can we just move heat? The premise of magic is that it takes "metabolic energy" and applies it as force somewhere else. Again, if we want to heat something, this seems okay, but to cool something, I keep winding up back at Maxwell's Demon.

Okay, so what we're missing is the entropic cost of cooling versus heating. If we're heating, it's not unreasonable to postulate that the entropic cost is zero, or very close to zero; after all, the net entropy increase is still $x$, we've just changed where that increase happens. If we're to avoid running afoul of thermodynamics, our best case scenario is that converting $x$ of "biofuel" into magic results in no net change in entropy. Thus, our best case would be that a magic user can transfer heat energy between two points with 100% efficiency.

...But again, our magic doesn't work that way. Our magic says that to apply $x$ force requires at least $x$ of metabolic input. It stands to reason, therefore, that our magic user trying to "cool" herself has to spend $x$ energy in order to transfer $x$ energy from her body to her body. This works; effectively she made her body metabolize $x$ worth of biofuel and convert it directly to heat (might be good for keeping fit!). This puts our "best case" for cooling at being able to lower heat energy somewhere by $x$ while increasing it elsewhere by $2x$. (No danger of replacing refrigeration, there.)

An Alternative

Maybe this isn't necessary. Maybe we can reframe magic as a transfer of energy in which the user is necessarily one of the end points. That would greatly simplify things; a magic user can cool something for no direct metabolic cost, but only by transferring the heat to themselves. This makes cooling in general really easy while putting a definite limit on how much a magic user can cool something without keeling over from heat stroke.

Initial Conclusion

It seems likely that the best case is that cooling a target by $x$ heats the magic user by at least $x$, and possibly more than $2x$, depending on which model we use. A more likely model seems to be that she has to burn some of her own energy just to "do magic", but that cooling works "in reverse", by pulling heat from the target into her own body, rather than doing the reverse (as when heating or moving something), so we're sort-of back at the heat pump model.

Refinement

Something I realized later is that transferring opposing forces from the magic user to a target to be cooled might not work. This is actually related to what happens when two atoms collide head-on; they lose their kinetic (heat) energy, but since that energy can't just vanish, it turns into photons instead; this is heat loss via radiation. If magic just makes this happen, then we can define it to work as follows: energy is produced via metabolism, which is "perfectly" paired up with the heat energy in the target in order to neutralize it, in a way that the resulting radiant energy all winds up elsewhere. This means that cooling something by $x$ produces $2x$ heat "somewhere", but presumably in the magic user's body, plus whatever inefficiency is inherent in doing magic in the first place.

I'd previously (and somewhat by accident) come up with numbers that would make magic 25% efficient (comparable to muscles). In what may or may not be a coincidence, this is the same efficiency as if we throw out the idea of being able to change the direction of force and calculate how much energy we can extract along a given vector based on random input (i.e. heat). This is equivalent to magic being optimally efficient using only the portion of heat-energy along the vector of the force being magically exerted. It also means that magic (i.e. telekinesis) doesn't violate Newton's Third; levitating a book "weighs down" the magic user in almost the same way as carrying a book without magic (the difference being how the force is distributed). The corollary of this is that using magic requires leverage. However, it also suggests that a) heating something is 100% efficient, and b) cooling something can achieve our previously derived "best case" where cooling by $x$ heats the user by $2x$, or, more optimally, heats both the user and something else by $x$ (while requiring more mental effort).

Takeaway

Our magic user won't be freezing any swimming pools (I knew that already, and I don't want that to be possible), but she can probably keep her beer cold (which was an objective).

I'd appreciate folks pointing out if I've done anything stupid here.

Footnotes

  1. The main magic user in my story is a female, so I'll use those pronouns.

  2. At least, I haven't been able to come up with a plausible explanation that isn't overly complicated. It would have to be something like compressing a ball of air, waiting for it to cool, moving it, then letting it expand again.

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