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.