# 'Magic' regeneration without breaking the 2nd law of thermodynamics

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.

Cheers.

• Perhaps approach it from a different direction: mages dont get more aether as they get experienced, but their spells more efficiënt. Spells would lose some energy the mage puts in and as mages become experienced they limit this loss, meaning less energy required for the same spell. Aug 9, 2018 at 22:47
• I think the 'Night Watch' book series by S. Lukyanenko uses a very similar explanation to what you describe. At least the German translation specifically talks about the 'temperature' of mages that basically determines how much magic they can draw/use from the environment (the lower their temperature, the more they can use). Aug 10, 2018 at 14:13

# The boring answer: mass-energy equivalence

You have seen this forumla before:

$E=mc^2$

This is not the work Einstein got the most scientific recognition for, but it exists in the popular consciousness. This is the mass-energy equivalence forumla.

Simply put: energy can become matter, matter become energy. This forumla tells us how much of each we get from the other.

• E is energy in joules (1 kcal = 4134 J, 1 kWh = 3.6 million J).
• m is mass in kg

The interesting bit — for you — is that c, which is the speed of light in vacuum... ~300 000 000 m/s. Square that... and you have a big number.

So from 1 kg of matter, you get 90 million billion joules, or...

## The entire energy output of a nuclear reactor for one year

Mass turns into a lot of energy. So if you want to maintain the laws of thermodynamic while at the same time giving your wizards the capacity to output lots of energy... the answer is: they get it by converting mass into energy.

Now this opens up an entirely different can of worms but you wanted magic, which — in the spirit of Arthur C. Clarke — is just: very advanced tech we just do not know how it works yet. The magic in this case is: some individuals can make energy out of matter without using a nucelar reactor.

• No discussion of entropy or thermodynamic principles.
– cms
Aug 10, 2018 at 16:21
• @cms And why would the answer need that? Aug 10, 2018 at 16:22
• Because that is the topic the OP is concerned with.
– cms
Aug 11, 2018 at 22:56
• @cms OP only asked for something that can give energy without breaking the laws of thermodynamics. Unless you claim Einstein did not know these laws and created a formula the breaks them... that was a very superfluous comment. Aug 12, 2018 at 7:20
• Your answer is only an alternative to the magic system OP is proposing. I am assuming OP wants a system where mages "stock" magical energy and liberate it to create whatever kind of energy they want. Your system is just converting mass into energy, which would mean that mages use the mass around them and convert it into other kind of energies at their will. That's a completely different thing to what OP is asking for imho. Aug 16, 2018 at 14:04

Concept

It could be done like vapor-compression refrigeration. So, magic is in the aether (analogous to the hot air). Your mage captures magic by means of some mediating substance, which doesn't necessarily have to be physical, but it has to be channeled in order to expose it to the aether, or else the aether has to be channeled to expose it to the substance (analogous to the coolant). The mediating substance absorbs the aether and changes phase after having absorbed enough of it. The mage then "recondenses" the mediating substance to its original form, releasing the magic back into the wild at a destination of his choosing, and it would just happen to be the case that "condensing" the mediating substance also converts some of the aether into actual energy in some manner. Pumping and condensing the mediating substance uses energy from somewhere (analogous to the electricity driving your AC).

So, here's an example of how this might work out:

Example

The mage activates his magic staff, creating a large dream-catcher-like glowing circle in the air. He's spent years training himself to use the energy stored in his body to pump aether through this circle. The circle is a window into the magical realm contained in the staff. As the aether flows into it, the magical properties of the staff are transformed from their inert state to a more energetic state, and the staff becomes visibly more powerful (if it's an organic staff, maybe it grows leaves or something; if it's a metal staff, maybe it glows). As he does this, the aether concentration in the environment is diminished significantly, but it will replenish with some time, and it never seems to be completely gone from any one place.

An experienced and well practiced mage is capable of channeling aether into his magic devices more efficiently, but some mages are just naturally better at it than others. It's like being a good runner; it's a muscle you exercise.

Later on, the mage once again utilizes his personal strength to catalyze the return of the staff's inner components to their inert state. This results in the aether being re-released in whatever form the staff is designed to do so. So, if it's a staff of fireball, the aether is converted into explosive energy in the real world, and some aether is lost back into the wild as part of the reaction. If it's a staff of ice, then perhaps the mediating material is such that a "condensation" reaction has to absorb heat energy in order to occur, and so much more aether is released into the wild at the expense of actual energy.

It doesn't have to be a staff, though. It can be a physical part of your body that you just don't use often. It could be part of your brain, or your hands, or your clothing. However you like.

Supplementary

Now, here's the thing. You've just converted aether into real energy (or v.v.) during that last step, so you've got to have a rule for conversion to or from aether. Maybe:

• E=mc2 (energy to matter)
• a=Ec2 (aether to energy)

So a small nuclear fission reaction converts a small amount of matter into a large amount of energy. And when mediating substances change state, it converts a large amount of aether into a small amount of energy. You might supplement this by supposing that aether is produced in the heart of black holes or antimatter stars or something like that. Maybe it's very abundant; maybe not.

Well that was fun. I hope this helps!

• Since I've never actually posted on World Building Stack Exchange, I can't up-vote your reply so I'll say here: much appreciated! Aug 10, 2018 at 0:12

Definitions: I will use the term "mana" as magic as in "magical energy", and "spells" as magic as in "to cast magic", to distinguish "magic" from "magic".

I would suggest mana would regenerate the same way we "regenerate" our energy IRL. The earth loses a lot of energy by infrared radiation, and even the energy that doesn't leave the earth, is "used up" - if you have a hot thing and a cold thing (e.g. steam & cold water), you can use that to generate energy, but at the end, the hot and cold are both lukewarm, and although the energy is still there, you can't get any useful work out of it, unless you add energy from outside (e.g. coal).

While there is a certain amount of usable energy "on earth" naturally (uranium for Nuclear Power), most of our energy comes from the sun, which is then stored temporarily in different forms, which we can unlock - solar is the most obvious from this description, but wind is indirect solar, as are sugars (which we get from plants, who generate it using solar energy), oil & coal (indirectly from solar, then concentrated).

None of these contradict thermodynamics - if your "system" is earth, then energy is coming in from outside the earth; if your "system" is the sun, then the energy in the system is running down - the sun has a limited lifespan, and the energy in the sun (a nuclear reactor!) is being used up. When it's gone, it's gone.

This gives you a lot to work with, I think - there's a source of mana, which is very difficult to affect, and any effect will both cover the entire globe (not just one wizard/witch), and is likely to be dangerous, so manipulating this is not a good idea. Direct use of the mana from it's source is limited (equivalent of solar panels) but ever-present (allowing a wizard with no resources at all to gradually gain mana little-by-little, at a speed for you to decide), but mana may naturally collected in various forms (easy to tweak the details to suit) which may be exploited.

When a certain amount of mana collected in one place, it might trigger "ambient spells" or "natural spells" without the presence of a spellcaster, using up the mana before it could collect too much; this might be inhibited by some sort of anti-spell substance or condition. In places where the anti-spell substance exists, mana would collect in greater amounts, until it reached enough mana to overcome, causing larger ambient spells, or "mana explosions". If such an area is discovered before the explosions, there would be a lot of mana to be harvested.

Ambient spells would be unpredictable, but I would expect that your easiest spells would be the ones most likely to occur as ambient. Environment & amount of mana would also affect which spells happen. With nothing inhibiting the spells, there might be a continuous spell which does almost nothing - perhaps a slight feeling of euphoria, consistent good or bad luck, specific weather, time running imperceptably faster, slower, irregularly, and so forth. Sufficiently large deposits of anti-spell ore might cause explosions, unicorns, an impassible wall, or anything else that can be caused intentionally by a wizard.

Hello from the physics SE. Since nobody has actually addressed any thermodynamic principles here, I will chip in an answer. Unfortunately, we probably need a bit of a primer first:

### Low entropy, not high energy, is the quantity of value

There are dense sources of energy all around us. For example: $$\begin{array}{l|c|c} & \text{Energy Density} & \text{Joules / kilogram} \\ \hline \text{Thermal Energy} (300K) & k_B T / \text{atom} & 2.4 \times 10^5 \\ \text{Chemical Energy (max)} & 13.6\text{eV}/\text{atom} & 5.2 \times 10^7 \\ \text{Nuclear Binding Energy (average) } & 6\text{MeV}/\text{nucleon} & 5.7 \times 10^{14} \\ \text{Rest Energy} & c^2 & 9.0 \times 10^{17} \\ \end{array}$$

In order to do any work, it is not enough to have a source of energy; that energy must be from a low entropy source. The definition of (classical thermodynamic) entropy is: $$\Delta S = \frac{\Delta Q}{T}$$ Where $\Delta S$ is the change in entropy of a system at temperature $T$ when it gains heat energy $\Delta Q$. Now, it is an observational fact that, for any closed system, the total entropy of the system will never decrease: $$\Delta S \geq 0$$ This is the 2nd law of thermodynamics. Along with conservation of energy, we can work out what the requirements will be for a magical effect to be consistent with those two laws:

Assume the magician $M$ can pull energy from the magical aether (denoted $\Delta Q_H$), and can then use that energy to do some amount of useful work (denoted $W$), along with any waste heat produced in the process ($\Delta Q_C$). To be consistent with the 2nd law, any magical process must produce some waste heat. If we take our closed system as the Earth plus the magical Aether, then conservation of energy requires: $$\Delta Q_H + \Delta Q_C + W = 0$$ and the second law requires: $$\Delta S_{\text{Aether}} + \Delta S_{\text{Earth}} \geq 0$$ We can combine these two equations to find requirements on the waste heat $\Delta Q_C$: $$\begin{array}{l} \frac{\Delta Q_H}{T_H} + \frac{ \Delta Q_C }{T_C} \geq 0 \\ \frac{-\Delta Q_C - W}{T_H} + \frac{ \Delta Q_C }{T_C} \geq 0 \\ \Delta Q_C ( \frac{T_H - T_C}{T_C T_H} ) \geq \frac{W}{T_H} \\ \Delta Q_C \geq \frac{T_C}{T_H - T_C} W \end{array}$$ If we take Earth's ambient temperature to be $T_C = 300 \text{K}$ and the magical aether to be something equivalent to sunlight (but perhaps much more energy dense and available 24-hours) then $T_H = 5000\text{K}$. Based on these values, then a magical effect which uses energy $W$ must produce a minimum waste heat of: $$Q_{\text{waste}} \geq 0.064 W$$ or roughly 6% of the magical effect.

### 1. Bringing mom back

If you want to raise someone from the dead in the style of the Elric brothers from Full Metal Alchemist, then you start with the base elements (carbon, nitrogen, oxygen, calcium, etc.). All your magic has to do from a thermodynamic standpoint is provide the energy in the chemical bonds. Using my estimate $5.2\times10^7$ J/kg of chemical energy, then for a 70kg person you need to produce $3.7\times10^9$J of work and $2.3\times10^8$J of waste heat. Water boils at a rate of $2.72\times10^{6}$J/kg. That waste heat is enough to flash-boil 189 pounds (85kg) of water, roughly a bath-tub full. (If there are any suits of armor around, avoid the temptation of putting the heat there. )

### 2. Turning lead into gold

Turning lead into gold would require separating up the protons and neutrons in a lead atom and rearranging them into gold. We get a some energy from the lead, but gold has more binding energy and so we will need to provide a net energy: $$\begin{array}{l|c|c} & \text{Lead} & \text{Gold} \\ \hline \text{atomic mass} & 207.2 & 196.96 \\ \text{Atomic Number} & 82 & 79 \\ \text{Nucleon Count} & 207 & 197\\ \text{Binding Energy per atom (J)} & 1.95\times10^{-10} & 2.19\times10^{-10}\\ \text{Binding Energy per kg (J/kg)} & 5.67\times10^{14} & 6.70\times 10^{14} \\ \end{array}$$ The difference in binding energy per kg is what the magician will need to provide so $W = 1.03\times10^{14}$J and the waste heat is $Q_C = 6.6\times10^{12}$J. Converting that waste heat to an equivalent amount of boiled water would be 2,410,000 kilograms, or almost exactly one olympic sized swimming pool, per kilogram of converted material.

### 3. I cast fireball

The standard Dungeons and Dragons fireball spell is a non-concussive (there's no explosion) sphere of fire 20-feet in radius. A 20-ft radius sphere has 1241 cubic meters. Air has a density of 1kg/m^3 so we can estimate the mass of the fireball to be 1241 kilograms. Then using the average thermal energy of matter at $3000K$ (10 times the value in the chart above) to be $2.4\times10^6$ J/kg, the fireball has approximately $3.03\times10^9$ Joules. Since there is no explosion, the work done in this case is zero. In this case, all the energy is spent as waste heat; put another way, the waste heat was the desired effect.

### Conclusions

Having you magical effects obey the 2nd law means they must produce waste heat. However it's up to the mage where the waste heat is created. This could be a useful byproduct in a war-setting. However, having to fart a fireball every time the magician wants to heal someone is problematic. I suggest differentiating the skills of your magicians at least by:

1. How much magical energy they can draw in a given time; some effects may just be too large for the novice magician.
2. How skillfully they handle the waste heat. This could be as simple as dissipating it into the ground or some other nearby heatsink, or more complicated if indoors and other exotic settings. It will be up to you how much of a hinderance waste heat is.
• I appreciate the inclusion of the mathematics! But yeah, I was planning on treating the Earth-Aether transition exactly how you proposed it above. Where the aether is in a much lower entropy state. The means by which I planned on regulating the powers of a mage/magician/wizard was by their 'efficiency' where energy is wasted. I've studied a bit of thermodynamics but not loads. I have to ask, could some of the wasted energy be rejected still in the form of aether somehow? On first glance I would guess it couldn't since the aether in the mage's surroundings would have roughly equal entropy? Aug 16, 2018 at 6:37

One possibility is that only certain physical structures in the body are capable of storing magical energy, or capable of storing it in some useful way. These structures are "exercised" by the use of magic, making them grow or develop to be more efficient, like a muscle. Although the energy is still in equilibrium, more of it is accessible to the user's power, either because it's channeled more efficiently or because more of them is capable of being tapped into.

This also provides an out for the traditional "some people just don't have magic, some are weaker, some are stronger", if you want that: clearly people just have better or worse genes for magic organelles in their family.

• This is essentially how arcane magic works in the 'verse I've written; arcana node in the brain, next to the amygdala. Controls ability to manipulate energy taken in my mages eating food (much like motor control and muscles). Easily triggered by fear responses due to its proximity to the amygdala. Aug 9, 2018 at 22:58
• @MatthewDave I'm not so much worried about how it works in the brain as in the body. I think that a structure you can exercise through use - like a muscle - works well for what the OP wants, regardless of the neurology of it. Aug 9, 2018 at 23:05
• Yeah, that's why I didn't bother making an answer, just a comment, heheh. With mine, I have it as 'magic is actually manipulating mutually quantum-entangled leptons that are orbiting pretty much every atom', and you need energy to manipulate them... which just comes from food, helped by devices that make said energy manipulation more efficient (the equivalent of 'wands'). Personally, I think 'energy from food' is a fine option for where magic comes from. Aug 9, 2018 at 23:19

I would visualize the Aether Field as a tablecloth laying flat, and individual people could be represented as rings laying on that cloth.

A person without magical talent only "contains" Aether at the same density as exists outside them; the tablecloth is flat both inside and outside the ring. They cannot do work with the Aether in this manner.

A mage, however, has to actively pull the Aether into their bodies, in the same way that a hand could tug the tablecloth up through the ring. The cost of this is the muscle energy required to pull the tablecloth upward. Similarly, the balancing factor of a mage is that their body must expend calories to actively draw the Aether into them, increasing its density within their bodies/souls/minds relatively to the background Aether Field. This allows them to do work with it.

For greater narrative flexibility, you a mage might be able to expend some of themselves (such as blood or body fat) to forcibly draw a large amount of Aether into themselves at once, rather than let it accumulate over time automatically (their body could burn the calories automatically, the same way it does to fuel their heart and brain, for example).

Skill and experience could still determine how efficient a mage is at drawing in or expending the Aether, as well as how much they can store.

• No problem, hopefully it's of at least some help with giving you some ideas. Aug 10, 2018 at 0:16

The system you talk about already has a parallel in the real world.
Temperature.

Humans frequently live in areas where the ambient temperature is lower than their body temperature, and yet we don't all freeze to death.
That's because we're warm blooded, we generate our own temperature. This doesn't break the laws of thermodynamics because it doesn't come from nowhere, it is generated by our bodies through the consumption of calories.

So what if your mages do absorb mana from their surroundings but only to the base level of the area. In more magic rich areas this base will be higher, in magic poor areas it will be lower.
On top of this mages generate mana themselves, constantly. Either through the consumption of normal food or through some kind of magical substance which contains mana as energy, just as we generate heat. Above the base level of magic mages lose mana as well so the generate it so the two rates balance each other out to a degree.

• Yeah, that is a good idea actually. I should have thought of that. Some kind of 'potion' (maybe not exactly a potion) which can temporarily increase one's access to the aether energy seems to fit in very well. Aug 10, 2018 at 13:08
• @JoeLee-Doktor Yes, the effect could be a temporary one instead of a permanent one if that's what you wanted. So before a battle mages would drink a potion or similar but the extra mana would slowly drain away to the environment if not used. Aug 10, 2018 at 13:18

Reverse the way magic is utilized

Mages don't actually expend magic, they manipulate the aether field. Instead of storing the magic within their bodies, they expell it, and utilize the now different concentrations of magic in the local aether field to conjure their spells.

Your problem, as it understand it, is analogous to the problem of heating a house (bringing the house above average temperature).

A magic potion may be considered a chemical store of energy in a form that only mages can successfully metabolize to magical energy (normal people metabolize it as sugar or not at all) - this would be the analogue to a stove-solution to the house-heating problem. Smaller scale analogues may include the kind of heating pillow that uses the heat(or magic...) of crystallisation of some medium (and later has to be re-heated/magiced).

Mages may be able to expend some (usual) energy on concentrating the ambient magic potential into themselves, analogous to a heat pump - as you have to place magic into the conversion diagrams anyways if you want it to be part of the physical world, you can as well include a ways to mirror the pV=kNT (pressure times Volume equals Temperature times a constant) of the real world, or extend it - pVM =TNk ? So under some circumstances it may be possible to locally raise the Magic by lowering the surrounding ambient Magic, with some inefficiencies that explain the lightshow and the inability of mages to operate in stuffy armor. Ambient Magic then later refills along the gradient.

If there is a conversion between Magic and any form of physical energy, you have to consider the that there usually is no going back - any matter or non-thermal form of energy is just a waystation en route to thermal energy. So either the Magic potential is constantly degrading since the Beginning, or you have to have a natural process that keeps up the ambient (Could be something cool like UV in the absence of certain longer wavelengths interacting with high-conductance metal that can absorb UV aka moonlight on slilver).

Do it in the same way life manages to exist without violating the second law of thermodynamics.

As long as your magic system follows conservation of energy (and preferably has some inefficiency), then you can draw that energy from anywhere. To give an example, the momenta of particles.

Assume our magic user can transfer momentum between particles (without creating or destroying energy, and with an inefficiency).

Say our magic user wishes to increase the temperature of a room. He can use the momentum of the gas in the room, supplemented with environmental momentum to account for the inefficiency and for an increase, to change the air's momenta and increase it. The room heats up. However, this is not a loss of entropy. While on the local scale, the room has lost entropy, it is not a closed system and global entropy, as a result of the environmental energy concentrated in the room, must increase.

It is analogous to life. To maintain life, and as evolution has dictated, decrease local entropy, we must draw energy from the external environment, specifically the sun. While on earth, local entropy has decreased, on a global scale of the universe, entropy must have increased.