Mobile Suit Gundam, as noted above. So famous are these particles (presumably because they are all-but unique in modern fiction) that Metal Gear 2: Solid Snake gives a cheerful Shout-Out to Mobile Suit Gundam by blaming the radar malfunction on 'Minovsky molecules.'
To note, the Minovsky Particles were designed specifically to allow or even encourage the existence of giant combat robots fighting hand-to-hand like ancient/medieval infantry (the biggest of which is messing with electromagnetic signals used in things like radar, preventing long-range targetting). The series creator has definitely read and possibly even written a few reports stating that with the advent of homing missiles, Drones, the ICBM and other automated weaponry, real-world modern/interstellar combat will take place at distances and speeds that make human involvement at anything past the planning stages dangerously wasteful, barring unpredicted advances such as the Minovsky Particle. This is also why he chose to use particle beam weapons instead of lasers.
Used as a Mythology Gag in the 2nd season of SD Gundam Force in the form of the Minov Boundary Sea, a gap between worlds that gets damaged when special attacks are used in it with unpleasant results.
Gundanium also merits a passing mention here, being an unspecified alloy that can only be manufactured by the Space Colonies. This sounds unlikely, but in actual fact is quite plausible, as liquid metal behaves very differently in microgravity. On the other hand, the official description of Gundanium says it contains several non-ferrous elements, something which isn't possible for a true alloy.
Also, in the CE timeline, the Neutron Jammer's side effects are a reference to the Minovsky Effect.
Gundam 00 has its own version in the form of GN ("Gundam Nucleus") Particles. Basically they do all the same things as Minovsky particles (produced via an exotic type of reactor, jam radar, allow non-aerodynamic machines to fly, and make beam weapons possible), along with a few new tricks (increasing the strength of armor and the cutting power of physical blades when they're impregnated with the particles). In the second season, GN Particles go from Minovsky Particles to magical pixie dust, capable of performing such feats as evolving a person, magically healing dying people, and teleporting mobile suits at will. While these changes are essentially unexplained the series drops hints of it in absolutely every episode, and some of the more "ridiculous" effects are simply extrapolations of previously observed properties. Basically, the 'true' (green colored) GN Particles had always been magical pixie dust in a sense but humans and technology didn't catch up for all of fifty-two episodes. Aeolia's convoluted Master Plan was intended to facilitate this catching up before his created assistants decided to go off on their own tangent.
In Gundam Build Fighters, the Plavsky Particles animate the plastic used to make Gundam model kits, as well as allowing them to produce realistic weapon effects like bullets, missiles, beam blades, and even explosions. While there are rigid rules, the writers themselves occasionally seem to forget them; it's said that Plavsky Particles only react with the specific type of plastic used in Gundam model kits, yet The Rival's Zaku Amazing was build using parts from a tank model which work with no justification.
Alchemy in Fullmetal Alchemist plays this trope pretty close, when you're not using a philosophers stone. While the second law of thermodynamics is thrown out the window, conservation of energy is usually held true.
Alchemists from Amestris learned alchemy from the sage from the east (Father) and think that their alchemy uses tectonic power. Alchemists from Xing learned alkahestry from the sage from the west (Hohenheim) and use ley lines. Xingese alchemists insinuate that the alchemists from Amestris don't have the full story and that something is "wrong" with their alchemy, and fans speculated that this was because Amestrian alchemy was powered by Father's stone. It's revealed that alchemists from Amestris do use tectonic power, but Father can limit or even shut off access to it by putting his philosopher's stone in the way as a barrier. This creeps out the Xingese, who can sense the souls from the stone writhing underneath the earth's surface. This is made much clearer in Brotherhood, where a piece of exposition explains the purpose of the nationwide reverse transmutation circle. It's there in the manga, the explanation just isn't as explicit.
Also, the Second Law of Thermodynamics is adhered to so long as there is some dumping ground for the entropy removed by reorganizing the matter. Presumably, part of the matrix involves the transfer of entropy from the object being transmuted to the surroundings. As for the first anime, Dante makes direct reference to the Second Law by referring to wasted effort- while input of matter and energy is necessary to achieve what you seek, it is by no means sufficient.
In the 2003 anime version, the first and second laws of thermodynamics are actually plot elements and not simply handwaved. Mass is conserved and the energy comes from death on the other side of the gate.
Digimon Tamers embraces this trope in a way that stands out from the rest of the franchise. In this series, there are only two fundamental changes to reality: Digital information can realise (i.e., literally become real in mid air) and actual artificial intelligence is not only possible, but has been achieved in the eighties. Furthermore, there is a great amount of detail put on explaining the working principles behind both (like the necessity for a converter algorithm). Otherwise, everything that happens in the series either obeys the rules of physics (especially because many of them did happen in Real Life) or is a consequence of the application of the Minovsky Physics.
Both the Marvel and DC Comic universes have plenty of examples. From Marvel:
Pym particles, named after Hank Pym which allow matter to be shrunk or enlarged at will, ignoring the square cube law and drawing extra mass (in the case of growing) from or shunting excess mass (in the case of shrinking) to another dimension;
Vibranium, an alien metal with two subtypes: Antarctic vibranium, which can destroy any metal by touch (even Adamantium) and Wakandan vibranium, which absorbs all kinetic force (including sound).
Adamantium, a (nearly) indestructible metal, only the strongest/most powerful heroes or villains can begin to damage it. It's a compound which is liquid until it sets, then stays in the given form forever. The robot villain Ultron (see below) is made of it.
From DC Comics:
Inertron (see below).
Promethium is a metal invented by Steve Dayton. When alloyed with titanium and vanadium, depleted promethium forms a near-invulnerable metal. Volatile promethium is also capable of generating near-limitless amounts of energy, and so can be used as a power source for many gadgets.
"Inertron" and "Ultron" in Philip Francis Nowlan's 1928 novellas Armageddon 2419 A.D. and The Airlords of Han, which became the basis for the 1929 comic strip Buck Rogers in the 25th Century. Both ultron and inertron are synthetic elements made of "ultronic vibrations" (which are akin to quarks in that Nowlan posits them to be to atoms what atoms are to molecules), which are "isolated from the ether and through slow processes built up into subelectronic, electronic and atomic forms" into miraclous substances with diametrically opposed physical properties. Ultron is "a solid of great molecular density and moderate elasticity, which has the property of being 100% conductive to those pulsations known as light, electricity and heat" and thus an invisible and nonreflective superconductor. Inertron is "completely inert to both electric and magnetic forces … has no molecular vibration whatever … reflects 100% of the heat and light impinging on it" and is thus not only a perfect shield against the Han Airlords' feared disintegrator ray but also an antigravity device, although that latter property involves a bit of handwaving in that it's never explained how inertron goes from simply having no weight to somehow having a negative weight, such that a sufficient amounts of it will either counterbalance a given weight, effectively making it weightless, or overbalance it to imparting buoyance. Left to itself, inertron "falls up" into outer space, presumably forever. Ultron would not only allow one to build the functional equivalent of Wonder Woman's invisible plane but, being superconductive, one should beware lightning and heat rays as well as disintegrators.
The "philotes" in the Ender’s Game series, which are particles that are the true building blocks of matter. They can be used to communicate instantaneously across space, and can be manipulated into new creations in "Outside" space purely on the power of thought.
"Swivels" in the novel El Caballo de Troia, which allow the time travel that the whole series is based on.
"Ice-nine" in Kurt Vonnegut's Cat's Cradle. Nothing more than a fictional crystal structure of ice, with specific physical properties similar to crystals of various other real-life compounds, it proves to be one of science fiction's most memorable MacGuffins. (Vonnegut worked in the marketing department of General Electric as a younger man, where his brother was a researcher. Said brother worked with Langmuir, who had much earlier dreamed up ice-nine for a visiting H.G. Wells, but nothing came of it.)
There actually is an Ice IX - "A tetragonal metastable phase" of water ice. However, it has nothing to do with the fictional ice-nine. The other wiki makes this distinction pretty clear.
The real version was the one used by James Blish's Cities in Flight, for building the Bridge on Jupiter. Under Jovian pressures and temperatures, "normal" construction materials like steel or concrete tend to melt, crumble, or otherwise disintegrate. In contrast, Ice IX is stable only under such conditions, but under human-compatible (that is, low) pressures, it would revert to one of water's commonplace phases.
Science fiction writer Larry Niven likes to explain the properties of all his Applied Phlebotinum in exquisite detail, often to the point of writing entire novels for the sole purpose of RetConning away flaws that readers find.
Found, of all places, in the form of Dust in the His Dark Materials trilogy. Dust, an elementary (read: indivisible, subatomic) particle can only be seen either when vast quantities are for some reason all brought together, or through special emulsions (which can be improvised using bamboo and seedpods from a different universe. Seriously.) Dust's most interesting quality, though, is that it attracts itself to sentient beings - anything made by humans to aid in thought and observation will attract Dust, such as a ruler, and Dust also attracts itself to people - adults especially, and the wiser the better. It has been implied that Dust is essentially meant to be the exchange particle (boson) for consciousness or conscious thought.
Isaac Asimov liked to use this, and several of his stories have produced standard plot devices for science fiction:
Asimov once wrote a mock academic paper (and eventually a sequel or two) about "the endochronic properties of resublimated thiotimoline", a substance with one chemical bond extending into the future, which dissolves before it actually comes in contact with water. (Pseudo-technical explanation: there's a carbon atom so sterically crowded that the only place one of its four substituents can go is through time.)
In a later Asimov story, a researcher tried to synthesize it, but accidentally produced antithiotimoline, with one bond extending into the past.
Asimov's novel The Gods Themselves takes the premise of beings from another universe sending an impossible isotope of plutonium into ours, and extrapolates the consequences to drive much of the plot. For instance, the other universe's physics leak into our universe along with the Plutonium-186...
The Three Laws of Robotics and their implications, of course, are also examined in detail, despite being described in-story as layman's simplifications of the Technobabble robots are designed around.
Played amazingly straight in most of the "Three Laws" stories which centered around robots apparently breaking one of the Three Laws but, in actuality, they were just taking logical extensions or interpretations that they humans didn't think of when they wrote them (or were failing to see circumstances that were obvious to the robots). Robot saving throw?
In fact, if you read Asimov's works, his robots gain progressively finer and finer interpretation of the Three Laws, culminating in R. Daneel Olivaw creating the Zeroth Law of Robotics - "A robot may not harm humanity, or through inaction, allow humanity to come to harm".
The Edge Chronicles has a few. These include substances that get lighter when you heat them up, to the point of reaching negative weight (some of them at room temperature, others need to be set on fire). There's also something called stormphrax, made of crystallized lightning, which has a bewildering number of strictly defined uses. Then there's a variety of rock which gets heavier when you heat it up, which (being buoyant in atmosphere at room temperature) is used to make ships fly.
Before writing The Mote in God's Eye Larry Niven and Jerry Pournelle asked physicist (Dan Alderson) to develop laws of their 'verse. They told him what they want the proposed FTL drives to do, and what they want to avoid. Dr. Alderson then custom designed a FTL drive to spec, with additional limits. Niven and Pournelle kept within those limits. As a bonus, Alderson's drive equations also got them Deflector Shields.
Kenneth Oppel's trilogy Airborn utilizes a fictional gas known as hydrium, a gas so much lighter than air it can lift practically anything. The internal consistency of its properties (technically, a gas as light as hydrium couldn't actually exist as an element) has attention called to it constantly.
Schild's Ladder pretty much runs on this trope, as it is based around the fictitious but believable "quantum graph theory" and the "Sarumpaet rules" that govern all fundamental interactions. It's been described as the "hardest science-fiction ever" with good reason.
He's gone quite a bit further with the trilogy Orthogonal, which takes place in a universe where spacetime follows the Riemannian rather than the usual (Minkowski) metric. (A minus sign is changed to a plus sign in one fundamental equation.) This leads to a raft of changes—light travels at different speeds depending on its color, and plants generate energy by emitting it, for one thing—and Egan has written a physics textbook as a companion piece.
In Robert Forward's Dragon's Egg, nearly all of the human technology that doesn't already exist today is based on magnetic monopoles. Given that Dragon's Egg is diamond-hard science fiction, you can bet that these particles are well known by the Real Life scientific communitynote While it's not known if they actually exist, physicists figured out their expected properties and there's an ongoing search for them, and Forward takes great care to explain the physics behind the technology employing them. When the Cheela develop technology, micro-black holes are nearly omnipresent in it. Of course, for a space-faring civilization whose members explode in a low enough gravity (as in, less than a few hundred thousands times Earth's), portable black holes are pretty much a must.
The Tom Swift series uses two: Tomasite plastic, which can block ionizing radiation and is a good neutron absorber/reflector, thus making relatively small nuclear reactors practical, and the repelatron, essentially a pressor beam with rigidly defined properties; for example, a repelatron tuned to repel sea water in a given location, creating a dry construction area for a helium collection plant, must be adjusted constantly so its output will be exactly right, or it could fail to repel the sea water. Worse yet, it could repel the blood plasma in the workers! Tomasite is also very strong, and can be produced as a solid, an air-cell foam, and a vacuum-cell foam.
A.K. Dewdney's novel The Planiverse is about a two-dimensional universe. In addition to discussing some of the expected technological issues (how do you build things when driving a nail through a plank necessarily divides it into two pieces?), he goes so far as to work out what impact having only two spatial dimensions would have on chemistry (the periodic table is different).
The FTL/STL drives in David Weber's Honor Harrington universe, which also have a secondary function as impenetrable shields over certain aspects of a ship's hull (as well as parts of the hull that can't be shielded when accelerating), and the limitations thereof, have repercussions in the design of ships, styles of space combat, weapons used, and customs of war that have show up constantly in the series.
Live Action TV
Star Trek absolutely, positively does not use this trope— writers were explicitly ordered to just have their technology do whatever the plot demanded, without even naming it. They were simply to write TECH on the script and let someone else on the production team fill it in with Treknobabble. However, it deserves a special mention only because it has a dedicated fan community that understands science and worked tirelessly over the decades to try to make the science of as many different technologies of the show as possible believable.
In the end, the only thing that seems to stick is that dilithium crystals regulate the interaction of matter and antimatter in the warp core to facilitate the creation of a stable warp field. The rest is Quantum.
Star Trek technical manuals do invoke this trope, though. They try to provide consistent explanations for the science and technology of the series. But the writers of the manuals specifically advise that anybody wanting to write a Star Trek episode or novel should avoid going into great technical detail, because that's just not what Star Trek is about.
Wormhole physics in the Stargate Verse. All of these rules and more are extremely important and show up multiple times throughout all three series. When something happens that goes against the usual rules, figuring out what special circumstances made it possible will be a main focus of the episode. See the exceptions described below, all of which were unknown to the SGC until they had first-hand experience with them. Some examples:
Matter can only travel one way through the wormhole: from sending 'Gate to receiving 'Gate. Energy (eg, radio signals) can travel both ways.note The one-way transfer of matter is a limitation of the gate itself. You can send matter through whichever way you like, but it won't be pretty.
A Stargate can only be open a maximum of 38 minutes (barring extremely high levels of energy or Time Dilation effects on one side)note the fact that the stargate can remain open longer than 38 minutes if one applies high energy levels to it suggests that it may be an engineering limitation rather than a physical law.
The wormhole cannot form if dense physical matter is in its way (eg, the Gate is buried, but air doesn't impede the wormhole forming).
Stargates only transmit matter in single, continuous pieces. An object will only be sent through once it's fully entered the event horizon. The corollary to this is that an object extending through the event horizon will force the wormhole to remain open until either its power is cut at the source, or the 38 minute window is reached.note As with anything that goes wrong with the stargate, the results of this are not pretty for the object.
Starfleet Battles is MADE of this trope. Every possible interaction of everything with everything else is specified in the (extremely thick, but also extremely well organized) rule book. If you need to know how an obscure system used by a handful of ships by one race in a minor corner of the galaxy interacts with another obscure system used on a handful of ships by a different race in a different corner of the galaxy when in a unique terrain feature found in a third corner of the galaxy...it's in there, and you need to look in a maximum of three places (all of which you need to read anyway to be using those systems and terrain) to find it. That also makes it a hard-core case of All There in the Manual.
Warhammer 40,000 paradoxically plays this straight and inverts it at the same time. Chaos, its go-to Applied Phlebotinum, has the distinct property of being unpredictable, but acts unpredictable given this by being, to a degree, predictable. It's consistent in its nature of being entwined with the soul, affecting people with high psychic aptitude and areas of chaotic influence, but exactly how it affects these people and areas when it does so is characteristically unpredictable.
The phrase "Mass Effect" is not just the title of the franchise, but an in-universe term for the Minovsky Physics surrounding the myriad properties and uses of an exotic matter called "Element Zero," which is the critical resource that makes interstellar civilization possible. Element Zero, or "Eezo" for short, increases the mass of nearby matter when positively charged (allowing for things like kinetic barriers and Artificial Gravity), and decreases their mass when negatively charged, potentially even to a negative mass (hence the name "Mass Effect"), enabling anti-gravity vehicles and a perfectly researched form of Faster-Than-Light Travel.
In addition, a ''lot'' of effort is put into making this incredibly fictional material believable, including (but not limited to): Doppler shifting and Cherenkov radiation by mass effect fields, the effects of overexposure to eezo, which range from fatal tumors to Bizarre Baby Booms of "biotics", and regular static discharges when eezo cores are used in space. The end result is the most consistent world BioWare has yet made. A lot of thought went into the resulting implications of the technology — for example being unable to use stealth systems at FTL speeds because of the effects blueshift would have. It even points out how the ability of mass effect fields to reduce an object to negative mass negates Time Dilation. Throughout all this, conservation of energy is strictly enforced, but the internal consistency is not perfect: conservation of momentum is not always enforced, and some of the telekinetic effects that biotics are capable of shouldn't be possible even by the principles of mass effect fields.
Biotic powers have nothing to do with magic, but are rather the result of having traces of Element Zero throughout the nervous system. As human nerves and muscles send signals through minute electrical pulses, the bodies of children exposed to great amounts of Element Zero during pregnancy become biological Mass Effect generators. Neural implants assist the brain in sending precise electrical signals to the Element Zero traced nerves to create the effects of "spells" near the person.
Kojima particles (or KP) are important for one reason: they are gaseous, but they act as solids when they colide with one another. Armored Cores generate and suspend clouds of KP around themselves to use as energy shields. This is called Primal Armor or PA. When projectiles or explosions pass through the PA, they compress the KP into its solid state, which allows it to slow them immensely or even stop them entirely. The Assault Armor function of PA has the AC eject its PA as a Sphere of Destruction. Anything in the path of the sphere will stall the KP and force them to crash into each other. Enemies hit by AA are essentially hit by a stone wall. Kojima weapons function similarly, only using beams of KP, missiles with KP payloads or "Kojima Knuckles". The use of KP for over boosting, however, goes unexplained.
Quite a lot has been established on the functions of Slipspace technology as well as the human and covenant weapons in Halo.
In A Very Long Rope to the Top of the Sky, the properties of saecelium are remarkably well-defined: it exists in the "liminal space between realities", and as such is fixed in spacetime relative to other saecelium; it outputs a fixed amount of power for a stable crystal of a given size; and fallout from unstable saecelium has (for the most part) known effects.
No Man's Sky utilizes an alternative periodic table of the elements to help with worldbuilding. Nothing much has been established on how it works, but it is known that it will help with making the procedurally-generated worlds unique due to how much or how little a planet has of an element.
Tratons in Unicorn Jelly, Tryslmaistan's equivalent of atoms. Instead of mass-attraction gravity, there's Linovection and Planovection, the Electanic Charge. She keeps up the habit in "Pastel Defender Heliotrope" with an entirely different dynamic system of Chatoyance.
Despite looking like A Wizard Did It, Lux in Tales of the Questor follows some rather specific rules and capabilities. Most of the underlying rules are only revealed by Word of God in the forums, but for a funky and surprisingly stable particle with rather specialized interactions with typical matter, its practitioners are still more intent on viewing it as a science than a matter of magic.
Magmatter from Orion's Arm is an incredibly detailed version heavily based on real scientific speculation.
Pattern theory, in the Whateley Universe. Used in order to explain where the energy for mutant superpowers comes from, and how mutants use it. It also limits the strength and scope of the possible superpowers, so a flying brick who can lift five tons is a really big deal.
Phaeton has several elements like this, icluding zero elements, which significantly reduce powers to the point of being useless, and memory elements, which when bent or even broken will return to their last safe shape.
Energon is a borderline case; while it was given many more powers than it used to have when it was made the focus of Transformers Energon, it shares certain properties that remain constant. It is an energy source for the Transformers that come in both solid and liquid forms, has Power Glows, and goes kaboom quite nicely when manhandled. In its natural state, though, it is unstable and gives off radiation that's hurtful to Transformers in large concentrations (though confusingly organic material is generally immune to it).
It's also the life blood of Transformers and Transformer life in general, as it's their fuel, the fuel for their weaponry, and used as currency. Any constantly-glowy melee weapon will also be called an Energon Whatever (presumably meaning it's powered by energon, rather than being made of the stuff, because stuff that explodes when struck doesn't make a good sword.) However, some series have somewhat different rules for the stuff:
Transformers Energon is a series where all the usual rules are kept, but it does a lot more, gaining New Powers as the Plot Demands, due to the amount of focus. We meet the Omnicons, who through millennia of Acquired Poison Immunity, can handle raw energon, and are the craftsbots who turn it into usable forms. Terrorcons, created from Unicron's body, can eat raw energon and generate processed energon. Energon Stars are the main form of processed energon, not cubes, and they can be plugged into Autobots, having the same effect as normal energon consumption in most series... or it can make new weapons appear out of thin air, heal massive damage as if by magic, and restore life to dead planets, mechanical and organic, and is said to be the building block of all life everywhere. Also, raw energon is yellow. When processed, the energon made by Omnicons and used by the Autobots is red, and is as deadly as raw energon - perhaps more - to Decepticons. Terrorcon-made, Decepticon-used energon is green and is similarly deadly to Autobots. Major Fridge Logic here - apparently, that makes the two factions different biologically somehow, and who knows what that means for when someone changes sides (If Wheeljack or Scavenger were still around, what kind would they use/avoid? And neutrals?) Oh, and letting the two types mix is very bad. There's also Super Energon - always liquid, will either supercharge you or kill you dead. Mind you, a lot (not all) of the unique properties of energon in this series, though not mentioned elsewhere, are also not contradicted.
In Transformers Prime the Autobots have been able to create synthetic energon, which can be a substitute for normal energon. Also, energon as "lifeblood" was usually symbolic, but liquid that is explicitly energon drips from wounded transformers in this series (fandom has long considered this to be the case, but it was not done onscreen until Prime, Prime also being the only series in which exposure to raw energon isn't harmful.note It's essensially Kryptonite for any Transformers in the other shows. Here, energon is food/lifeblood/fuel/etc, and consumption of raw energon has proven to be a useful substitute in cases where the liquid, processed thing is unavaiable - albeit a subpar one. Notably though, the series does establish that energon is very harmful to humans if it comes into contact with our nervous systems.
In Beast Wars episode Power Surge, the Predacon Terrosaur, is running low on energy and is far from base. He gets a charge off a surface-exposed chunk of raw energon. It powers him up and how!, but repeated use proves addictive and nearly fatal. This ties in with raw energon is dangerous to Transformers.