What would happen if magic was constrained by the second law of thermodynamics

Question

This is a followup question to the question Wondering what would happen if magic was constrained by Conservation of Energy and it's related to this post. This question asks which sources of energy could feasibly be tapped by magicians, and the answers there compliment the answers below. In this question, I would like to know the specific restrictions on using those energy sources, where the second law of thermodynamics holds¹.

The second law of thermodynamics states that:

the entropy of an isolated system never decreases, because isolated systems always evolve toward thermodynamic equilibrium, a state with maximum entropy.

I will borrow wikipedia's definition of magic:

Magic or sorcery is an attempt to understand, experience and influence the world using rituals, symbols, actions, gestures and language.

Naturally, this question will focus on the abilities of magic to influence the world. For the present discussion, assume that magic also encompasses superhuman powers.

Are there clear rules based on science which dictate if a hypothetical magical process, event, trait, or ability would be possible in a world where magic is constrained by the second law of thermodynamics?

Concrete examples of how one might go about deciding which processes are possible would be very helpful. I would also prefer answers that deal exclusively with Newtonian physics; I think it's going to get a little too complicated if we try and bring in relativistic effects.

Also, please assume that the conservation of laws of mass, momentum, and energy also hold.

Finally, there should be no reference to other dimensions or other universes to which entropy may be 'dumped'. Any world involving magic is can use this as a workaround to try and explain things, although this is not physical as far as we know.

^{1 The first law of thermodynamics is another name for the conservation of energy.}

Answer 1

There's a quick summary at the bottom; read the rest for a better understanding.

Spoiler Alert! I discuss characters from The Incredibles and X-Men: First Class with reference to the plot events. You have been warned.

Better Evaluation Criteria

First of all, it is hard to evaluate the plausibility of a magical process by reasoning whether or not it violates Wikipedia's definition, because that definition applies to an isolated system, and I believe that most magical processes occur in open systems (i.e. mass, energy, and entropy may be exchanged with the environment). An easier way to evaluate second law violations is to question whether a system violates one of two statements, which cover most second law violations.

Clausius Statement

Heat can never pass from a colder to a warmer body without some other change, connected therewith, occurring at the same time.

The first part, Heat can never pass from a colder to a warmer body, is eluding to Fourier's Law. We have always observed that heat moves in the direction of the highest temperature gradient, or from warmer regions of a substance to cooler regions. The spontaneous movement of heat from cooler matter to warmer matter is widely regarded as impossible. A device which violates the Clausius statement is shown in the figure below.

Modified from "Deriving Kelvin Statement from Clausius Statement" by Netheril96 - Own work. Licensed under CC BY-SA 3.0 via Wikimedia Commons.

We do have devices that move heat from cool reservoirs to warmer ones; they are called refrigerators, but they require an external work input. That's what the exception therewith, occuring at the same time. is referring to.

Kelvin-Plank Statement

it is impossible to devise a cyclically operating device, the sole effect of which is to absorb energy in the form of heat from a single thermal reservoir and to deliver an equivalent amount of work.

This statement describes a machine which absorbs energy from a high temperature reservoir (e.g. a boiler), and exports all of that energy as mechanical work (e.g. a steam turbine). This is another device which satisfies the first law, but not the second law. To understand why this is an issue consider the figure from wikipedia:

"Deriving Kelvin Statement from Clausius Statement" by Netheril96 - Own work. Licensed under CC BY-SA 3.0 via Wikimedia Commons.

The imagined engine is the Kelvin-Plank engine on the left, where the mechanical work output powers the refrigerator (Carnot Engine) on the right. The refrigerator does not violate the Clausius statement because it has a work input. But since we don't have any real restrictions on what constitutes a 'device', the combined device (dashed green line) should also be possible. The simplified device is shown in the first figure.

This device has a net work input of zero, and at the same time it still moves energy from a cooler reservoir to a warmer one. We can now see that it implies that heat can be moved from a cold reservoir to a warmer one without an external work input, which is impossible.

Both of these statements describe machines which violate the second law, and either can be used to evaluate the plausibility of a process¹. We can see that, in general, these statements help us eradicate designs which suggest that heat spontaneously flows from cooler reservoirs to warmer ones.

Examples

I'm now going to analyze two superhumans from recent movies and use the above statements to decide on whether their powers violate the second law.

Frozone: (The Incredibles - 2004)

Frozone is a 'Super' from the Incredibles' universe. He utilizes moisture from the air and his own body to freeze parts of the environment. First let's just consider the moisture absorbed from his own body.

We can realize pretty quickly that Frozone is just a really efficient and high powered ice machine or ice maker. He extracts heat from a low temperature 'reservoir' (the stream of ice shards coming from his hands) and dumps the heat to the surrounding environment (assuming his body temperature is constant). There is nothing wrong with this; there is just some crazy refrigeration system that is a part of his physiological makeup which allows him to do this.

But what about the ability to absorb moisture from the air? It turns out there is a similar form of Fourier's law (heat always flows from hot to cold) that applies to mass transport called Fick's law, which dictates that diffusion of a species (e.g. water vapor) in a fluid will always occur in the highest concentration gradient. Again, similar to heat transfer, we can't create a device that moves mass from a low concentration reservoir (ambient air) to a high concentration reservoir (Frozone's body) without external energy input. But he can do it so long as he can supply sufficient energy input.

Verdict: Plausible We know that refrigerators work and dehumidifiers work, so Frozone's ability seems plausible, so long as he can supply the energy required.

Sebastian Shaw:

(X-Men: First Class 2011)

Sebastian Shaw is a mutant from the X-Men / Marvel Universe. He has the ability to absorb energy from various sources and release it in alternate forms. For the most part he seems to garner his power from kinetic energy sources, but I'm going to pick on the event towards the end of the movie, where he locks himself in the mirrored nuclear reactor chamber and absorbs the energy from the fuel rods by grabbing hold of them.

For this analysis, the nuclear fuel rods can be considered a constant high temperature reservoir. During this scene, he doesn't perspire, suggesting that he isn't losing any heat to the environment, and there's no evidence of significant heat loss by other means. Shaw himself is the 'engine' who is storing energy for later, and as I have seen in other scenes in the movie, he has the ability to use his absorbed energy for kinetic attacks; i.e. he can do mechanical work with the energy. Is this raising any concerns? We have heat engine (Shaw) who is gaining energy from a high temperature reservoir (fuel rods) while dumping a negligible amount of heat to his surroundings (floor and ambient air), where the vast majority of it can be used to do mechanical work.

Verdict: Busted! Given what we are told about Shaw in First Class we can almost certainly conclude that he is behaving as a machine which violates the Kelvin-Plank statement, thereby violating the second law of thermodynamics.

Other Implications

In the last section I talked about the movement of mass as another process which only occurs spontaneously in one direction. There are other forms of transport such as electromagnetic and nuclear are bound by similar restrictions.

Summary

The common thread is the concept of diffusion; anything that tends to spread out over time will not spontaneously concentrate in a single place.

Here are some basic questions you can ask yourself to help determine whether your magic obeys the second law of thermodynamics (as the real world does):

• Are there any real world devices which do what this magic is doing? If so, then your magic is plausible. It might be more powerful and more efficient than any devices humans have invented, but that's acceptable. This is the easiest way to validate the magic.
• Does it Violate the Clausius statement? Is there a magical rod which always moves heat to one end? Is there a certain wizard who can draw poison from a wound? Can a caster absorb energy by freezing a lake of water? Is there an enchantment which directs airborne viruses into the airways of unfortunate recipients? These are examples of processes which are the reverse of diffusion; they are moving stuff to a desired region of space. They are possible, but they always require an energy input.
• Does the magic violate the Kelvin-Planck statement? This one is trickier to spot. If the magic uses thermal energy to do some mechanical work or store energy, there just needs to be a lower temperature reservoir where some heat is being dumped, so the process is not 100% efficient. In the example above, if Shaw's hands were sweating a little when he grabbed the nuclear fuel rods, it would show that some heat is being lost to the environment, and for me personally, that would have made the scene more believable. As for how much energy must be dumped, it depends on the process, and that's a more difficult question to answer. Right now I will just say that it shouldn't be insignificant relative to the energy gained from the process.
• Still think there's something unbelievable about the magic? Post your question on this site! There's a lot of details I've omitted and there might be some very common cases that are worth addressing in a separate thread.

^{1 Note that the statements are, in fact, equivalent, and any device that violates the Clausius statement also violates the Kelvin-Plank statement.}

Answer 2

The concept of entropy in thermodynamics is intimately linked to the concept of energy, therefore I think the answer to this question depends on the answers of a few other questions:

1. Does magic use a separate "magical energy source", or does it just work by redirecting energy flows from existing sources?

2. If a separate energy source (like a "magic field" or similar, that only magicians can tap) is used: Is the magic energy resource work-like (the magician can remove — and possibly even store — energy in it as he wants), or heat-like (the magic reservoir effectively has a temperature, and withdrawing energy from it is limited by that).

Let's consider the three cases separately.

Pure energy redirection

If the magician doesn't have special magic energy sources, then thermodynamics mostly enters when he affects heat, in which case he actually acts as a heat engine or heat pump. Like any heat engine, he would be restricted by the Carnot efficiency. Especially, he could not cool anything down without either a cold reservoir where he could direct the heat into, or an energy source he could tap in order to actively cool the object; in this case, he additionally would need to dump the heat plus the needed work drawn from that other energy source. If that other energy source is itself heat (which then has to be hotter than the environment), also his harvesting of energy from that heat source is limited by the Carnot efficiency; for example if he's in an uniformly hot place, and any colder place is outside the reach of his magic influence, he cannot harvest the energy in the heat for anything, be it cooling or something else.

Heat-like magic energy source

If there's a separate source of magic energy that has the characteristics of a heat reservoir, then of course in principle the same rules apply; except that as long as the environment's temperature doesn't match the "magic temperature" he can use that difference for his magic (if interacting with the magic reservoir is the only way to do magic, this would also mean that if the environment's temperature matches the magic temperature, he would lose all his magic power).

In this scenario, the magician could change the general temperature of the environment in the direction of the magic temperature by just letting energy flow between the environment and the magic reservoir. Especially if the magic reservoir is colder than the environment, he could seemingly violate the second law by cooling the environment without apparent other change (since ordinary people would have no clue about the magic reservoir). He would also appear to violate energy conservation that way, even if he really doesn't, since the energy flowing to the magic reservoir would be invisible. Of course, he could also turn part of that energy to work, but restricted by the Carnot efficiency; in effect that would mean he'd always deplete the non-magic world of energy whenever he does magic.

If the magic temperature is higher than the environment temperature, then just letting energy flow between the environment and the magic environment would heat up the environment. Of course, again he could convert part of the heat drawn from the environment to work, but not completely; any magic would be accompanied with heating up the environment, and using energy which apparently comes from nowhere. If he would want to cool down things, he'd have to use the work extracted for effectively heat pumping, which then again is restricted by Carnot efficiency; cooling down some part of the environment would need heating up another part much more (in part to harvest the work from the magic reservoir, and in part from converting the harvested work into heat during the cooling process).

Of course if the magic temperature is such that it is sometimes below and sometimes above the environmental temperature, the two cases may apply at different times, and at certain times the magic ability may be completely disabled due to temperature match.

I think that would be the most interesting option.

Work-like magic energy source

This one is actually quite simple: The magician could tap the magic energy source just like some engine might draw energy from a flywheel. If the magician can only draw energy out of the magic energy reservoir, he would inevitably heat up the world during magic (there may, however, be processes which refill the magic reservoir from normal energy sources). If the magician can also store energy into the reservoir, he could also tap energy sources in the environment to refill it. However, if he taps heat sources, he'd still be bound by the Carnot efficiency.

Answer 3

I would argue that nothing would change if "magic were constrained by the Second Law of Thermodynamics" because all modern fictional magic systems are already constrained by the Second Law of Thermodynamics. If they weren't, there wouldn't be a story. Authors just have to be sneaky about how they work it into the magic.

The Second Law defines our existence. It drives evolution which in turn lays the foundation of human behavior. By forcing us to expend energy to accomplish anything, it limits the actions we can undertake and forces us to make choices between alternatives. Our intuitive understanding or human behavior and our evaluation of human actions encode a gut understanding of the Second Law even if we know nothing about the math or science of it.

A character whose travails a reader can empathize with must wrestle with the Second Law. Characters wholly not subject to the Second Law don't seem powerful, they seem utterly inhuman and ineffably alien. By extension, any fictional world restricted by the Second Law, even in just a part, feels fake and unbelievable. If the world feels fake, the so does the characters. With no strong characters and no reader empathy the story fails.

But, the appeal emotional appeal of magic in a story for a reader arrises marvel of seeing the effects of breaking the Second Law. The Second Law restricts and burdens us, we like to fantasize we could escape it (as in the modern search for Free Energy.) Magic fulfills this desire in fiction.Mages create objects "out of thin air," see the future, alter the past, live forever and perform other feats that explicitly violate the Second Law. Arguably, violating the Second Law, is what makes magic, "magic." To have magic in a story, the author must depict explicit violations of the Second Law as readers intuitively understand it.

Authors confront a paradoxical story requirements. To create a believable world, the Second Law must be as universal as it is in the real world but to provide surprise, awe, wonder and the emotional appeal of magic for the reader, the magic system must be able to violate the mundane Second Law that readers encounter every moment of their real world existence.

The solution is to shift the "cost" of complying with the Second Law from physical systems to the characters themselves. The reader relates to the character's struggles against Second Law limits, not the Second Law's restraint on the inanimate environment. The story will satisfy if the character struggles with limitations that to the reader feel like the limitations imposed by the mundane Second Law. The source of those limitation is largely irrelevant save for stylistic purposes.

In magic systems of both traditional cosmologies and in modern fiction, the role of the limitation of the Second Law on the character takes the form of a "price" the character must "pay" to evoke the magic. The price can take any form as long as the character must must struggle to pay it.

For example: A mundane car pays one of it's Second Law prices in the form of fuel and provokes no awe or wonder while a car that requires no fuel feels instantly magical to the reader. But a car a car that imposes no cost on the characters using the car, breaks the readers intuitive Second Law model of the world and feels wrong. Often readers describe such magics as shallow, tinny, silly, comical or childish. The appearance of such magics "breaks" the reader's model of the fantasy and yanks them out of their immersion in the story.

The author fixes the car's world breaking by imposing a price on its use that the character must struggle to pay. The price serves the function of the limitations imposed by the Second Law in the real world, making the car feel like it belongs in human affairs and thus making the character interacting with the car feel more real as well.

The price can take any form as long as it requires the character utilizing the car to expend time and energy in the same way they would have to expend time and energy to obtain fuel for a real car.

For example, the character might have to sing a song to the car constantly to induce it to move. While singing the song, the character cannot perform other task. At some point in the story, the need to sing to drive will conflict with some other need or desire and impose a limitation on the character that the reader will intuitively empathize with. The need to sing serves the function of the limitations imposed by the Second Law in the real world.

The car now overtly breaks the mundane Second Law and provokes wonder, "look the car moves without fuel!" but still imposes Second Law restrictions on the character so that the character's conflicts, choices and actions feel human and realistic enough for the reader to empathize with the character. E.g. After a while the novelty of moving the car by singing grows wearing. The character needs to cast a verbal spell at the same time he needs to move and must choose between needed actions. The character grows hoarse.

Magical belief systems and modern fictional magical systems have come up with a lot of different types of Second Law mimicking prices. Most magical systems use some combination of prices instead of relying on just one. Below are few off the top of my head.

Violation of Mundane Second Law Causes Problems The magic breaks the Second Law and appears wondrous but that breaking the Second Law collides negatively with the rest of the story world which still follows the mundane law. The conflict causes the characters to exert mundane time and energy to manage the these side effects.

For example, a sword that will cut anything with zero effort appears wondrous but quickly causes negative side effects the character must struggle against precisely because it cuts everything whether the character wants it to cut that thing or not. He must contrive to sheath it or otherwise carry it safely despite the fact that nothing can touch the blade edge. If he drops it, it will bury itself in the ground to the hilt, drop through wooden ship's hull. When wielding the sword, the character cannot strike himself, an ally or an innocent without instantly cutting them. Fumbling the sword could be lethal.

The expenditure of mundane time and energy to manage the side effects serves the function of the limitations imposed by the Second Law.

Rarity, Usually with Limited Function: The magic is very, very rare. Superficially, the magic has no price but it takes an enormous expenditure in time and energy on the part of the character to actually obtain the magic. That expenditure serves the function of the limitations imposed by the Second Law.

Rare Material Components: Often seen in traditional sympathetic magic. These components are hard to obtain, often unique or specific to a place, object or individual, single use and do nothing more than provide information, the sympathy, to target the spell or give it specific qualities. The difficulty of obtaining the specific material components serves the function of the limitations imposed by the Second Law.

Human sacrifice: Using humans as a means of enabling spells obviously limits mages owing to humans natural tendency of desiring to avoid being the sacrifice. Sometimes a rare or sacred animal creature or object, something unique and hard to obtain serves as well. The struggle to obtain sacrifices limits the amount of magic the mage can perform and serves the function of the limitations imposed by the Second Law.

Time: the classic D&D limiter of making mages spend hours every day memorizing spells. Since there are only so many hours in a day, this price limits how much magic a mage can perform per unit of time. The need to trade time, a limited resource, for magic, serves the function of the limitations imposed by the Second Law.

Ephemeral/abstract quantities: Something abstract and non-material that that has no readily apparent mundane Second Law value but which have some conceptual limited quantity. Parts of one's soul, memories, future potential, life span, mental pain etc are all abstractions but ones without infinite quantity. A mage only has so much soul, so many memories, so much future, so much life span and can only tolerate so much pain.

To create a magical effect the mage must decide if the value of the effect warrants the percentage of the abstract quantity he must exchange for it. That need to husband the abstract quantity serves the function of the limitations imposed by the Second Law.

Logical Deal with the Devil: The mage must bargain with or coerce a magical entity to perform feats which violate the Second Law but the entity will not perform said feats except as strictly required a logical construct in form of a contract or precise instructions.

Usually, the entity is actively malicious and seeks to harm or frustrate the mage by exploiting any ambiguity or loophole that mage mistaking leaves in the logical construct. The time it takes to construct the logic, it's unpredictable interpretation by the entity and thus the resulting effects, topped of with the very real danger of the entire process, serve the function of the limitations imposed by the Second Law.

(... in the real world it's called programming. Yes, computers are actually malicious, inanimate machines my %$#@!. Just ask any programmer.)

Shamanistic Trading Magic: In this tradition, common in the world's smaller scale cultures, everything that exist is controlled by a spirit with personality and desires. Shamans can convince the spirit to perform task by trading the spirit something, sometimes an objects, sometimes ephemeral, sometimes getting another spirit to do something. I

In may stories, the mage must weave a complex web of trades with many spirits to end up with the particular trade item valued by the one spirit that can do what the shaman wishes done. Often combined with the Logical Deal With The Devil in whole or in part. The complexity of the trades, the time it takes and often the danger of dealing with the spirits, serves the function of the limitations imposed by the Second Law.

Time and/or location restraints: Classical concept in which magic is only possible when the stars align and/or on certain dates or at specific locations. Often combined with another restraint like Sacrifices. The mage can't just act at any time or place of his choosing. Mundane acts that block access to the location or prevent the mage from evoking the a the stop the magic. The effort of evading interference serves the function of the limitations imposed by the Second Law.

Limited knowledge: Based in the oldest traditions dating back to Sumerian-Sanskrit Ur magic, which form the roots of most Indo-European magic concepts and the basis for our concept of a "spell." (The most interesting price in my opinion.

In this magical system realty is defined by language i.e. specific words, with specific pronunciations and/or spelling/glyphs, within a specific syntax, define reality itself. By speaking/writing/inscribing the correct forms of words in the right syntax directed at the right part of reality, the mage order the addressed part of reality to assume whatever state he wishes.

In Ur magic, true words are not symbols, they are reality itself, the only true reality.

In Genesis, God commands, "Let their be light" and there is light. This concept of god creating by word alone is of the Sumerian tradition (secularly speaking.) A mage who learns the true name of light as spoke by God can create light at will.

In the classic golem story, writing the true word for "life" on the clay golem causes it to adopt the attributes of being alive while altering the name to spell "dead" causes it to lose the attributes of life.

Knowing an object's, creature's or individuals true name, the name that marks it as unique in all of realty, gives the mage complete control over it.

The Ur magic is the origin of the idea that, "words have power". Today we mean it in terms of the ability to skillful use words to persuade other humans but originally it meant the ability alter reality. The Word of God in the times of the Old Testament was not just moral commands but defined and sometimes altered reality.

Humans cannot discover true words on their own. Usually humans learn of them initially only from mystical beings who taught them to humans in the distant past. Overtime the words are forgotten. The mage must struggle to recover and understand them.

Since the true words are reality, not symbols, speaking, writing or inscribing the true word in the proper form and syntax instantly alters reality. The true words cannot be communicated directly and openly e.g. "Okay, pupil the true word for 'fire' is Eq Um So...ahhhh! water! water! water!" Neither can they be written e.g. "Chapter 3, Fire. ...ahhhh! water! water! water!"

(In Norse Runic magic, the inscribing of the runes creates their effect on the object or place so inscribed. That is were the tradition of runes etched into weapons comes from. Runes where memorized an only actually written when used.)

Masters have to instruct apprentices purely by example. The master says the true words and alters reality while the student watches. Then he must try and duplicate the master without further instruction and/or killing himself. Written knowledge of true words must be couched in euphemism and allegory.

Mages had to struggle to learn the true words and once they did so, had to devote them solely to memory relying on mnemonic devices to help them remember. Putting the words in rhyme was an obvious memory aid. If a mage died without passing his knowledge on training apprentices by example, then the explicit knowledge of the true word died with him.

All the difficulties of preserving, finding, learning to use the true words and names serve the function of the limitations imposed by the Second Law.

---

The art of good fantasy world building lays in actively weaving the limitations of Second Law tightly throughout the magic system so that the system feels "real" while disguising it so throughly that the magical effects themselves like wondrous violations to the reader. The reader must experience the wonder of breaking a universal law of our reality but at the same time must empathize with the struggles of the characters against the magic's limitations.

The fact that we can ask a question like, "what would magic be like if obeyed the Second Law?" is an indicator of their success in doing so.

Answer 4

You would probably get something like Fullmetal Alchemist

Fullmetal Alchemist's brand of magic (alchemy) is very explicit about matter/energy never being created or destroyed- referred to as the "Law of Equivalent Exchange". All transmutations which result in a lower entropy or higher energy state must receive energy from somewhere, which in most cases is tectonic energy. Transmutation circles act as a way to channel this energy into reconfiguring the natural elements around them. Mass is meticulously preserved in every normal transmutation throughout the entire series. (Though one scene in the 2003 anime cheats a little with Edward changing his prosthetic arm to different metals, which wouldn't really work due to the different densities of those metals)

There are also "philosopher's stones" which appear to sidestep the second law of thermodynamics, but even these are limited. They derive their energy and matter from human life force (Einstein helps us out here with his famous Mass-energy equivalence law) and will stop working as soon as all of the life energy has been consumed.

As noted from another answer, storing the energy in a compact form like a philosopher's stone isn't going to work because it would either need to be extremely hot or store the energy in some sort of ethereal form (which is not allowed by your question), but you're still left with a pretty versatile and powerful magic system without philosopher's stones.

Answer 5

The second law would only be an issue if you tried to use magic in a way which would actually increase entropy, like by splitting temperatures into hot an cold. We can consider conservation of energy a seperate issue.

Let's say you want to boil a kettle. Would this increase entropy? Yes! This would make the temperature of the kettle different from the surroundings, since the surroundings would be at the same temperature. Some of the various sollutions to the problem of Maxwell's demon, a device that has a door that opens only for certain types of atoms, and the reconciliation of the problem with the law can offer us some guidence to how magic can be reconciled with entropy. One solution is that the demon's memory increases in entrop, and in a magic system, too, a similar thing could be done where entropy is essentially moved around, so that, rather than just the kettle boiling, you could also melt an ice cube to make there be a bit more order nearby, you could also have the magic automatically mix finely sorted powder, mess up a stick into goo, or run on a sort of entropy fuel like machines run on energy. The entropy would be moved from the kettle's temperature gradient to the stick's mollecular structure, and since this is fictional magic, you can just decide these things, and that's that!