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In science fiction there are often these so-called "alien resources" found only on certain planet(s). How would this be plausible considering majority of complex elements are formed within stars?
Most easily explained theory would probably be uneven elemental distribution in universe due which not all elements are found in all places, but what kind of an astronomical scale event would create such diverse conditions on planetary scale?
Assuming that laws of physics are the same throughout the Universe, the periodic table will be the same everywhere. Thus it's hard to justify existence of "alien atoms" e.g. infamous Unobtainium
Instead of atoms I'd try to use molecules. For example, oil or Chitin must be pretty specific to Earth as it's a product of local organisms and millions of years of time.
Also you can view human brain as a limited resource: fat-based sugar-powered substance that is capable of cognition. (only 7 billion units for the whole galaxy!)
In summary, something that requires lots of time or lots of energy and a particular environment should do as an "alien resource".
This question is a version of the kryptonite problem. Namely, how can a green glowing metal or mineral substance exist that can produce a form of radiation that robs kryptonians of their super-powers? Kryptonite and its radiation is plainly contrariwise to nature. This works in comic books where most of their "science" is purest hand-waving or rock-solid pseudoscience.
For the purposes of teasing out this question of "alien resources" it will be assumed there exists 'exotic substances' with high technological or economic utility. This could be apparently contrary to nature as we know it.
However, there is one class of high value and high utility substances that exists here on Earth. Various biological compounds that can be used as drugs, antibiotics. medication and stimulants. They are usually found in plants, but animals also produce interesting compounds. The marine environment is becoming the next environment for research to find such new compounds. Within reason, we can expect the biosphere of any planet will have substances that might be effectively unique. Wherever results in finding Frank Herbet's spice on Dune or Cordwainer Smith's stroon On Norstrilia is a moot point, but biological subsatnces have great economic and practical utility. This qualifies as one class of "alien resources". This doesn't require astronomical scale events for their creation. Finding them will take considerable field work.
Now for the truly 'exotic' classes of "alien resources". Unobtainium could originate in other universes where the physical laws are somewhat different, but sufficiently similar that matter from those other universes can exist in our universe too.
How they got here requires something more than astronomical events, this involves cosmological events -- when universe collide! Taking our cue from M-theory and the notion that universes are branes that exist in a kind of hyperspace called the bulk.
Some versions of brane cosmology, based on the large extra dimension idea, can explain the weakness of gravity relative to the other fundamental forces of nature, thus solving the hierarchy problem. In the brane picture, the electromagnetic, weak and strong nuclear force are localized on the brane, but gravity has no such constraint and propagates on the full spacetime, called bulk.
It has been conjectured that branes (or universes) can move around in the bulk and are liable to collide with each other. This is the point where this answer makes a leap of scientific plausibility and proposes that matter is exchanged between universes during collisions. This extramundane matter will have 'exotic' properties compared to normal matter in its host universe (since it originates in another universe). It is also assumed that the exchange of matter only takes place in relatively localized portions of each of the universes.
This could result in certain planets being the only source of specific forms of valuable unobtainium. Please note certain assumptions were made to "tweak" current science to build a model to lend plausibility (of a sort) to the concept "alien resources" being found rarely in the universe.
I think, that thinking about these as "elements" instead of compounds is fundamentally flawed.
The list of elements is pretty fixed an pretty well known, it's governed by the weak nuclear force and how it binds atomic nuclei together. This governs how stable a given element is and what its atomic number is. A brief and simplified description of the weak force and the stability of atomic nuclei, is that the proton has positive charge. Like charges repel so when you get so many protons packed together their positive charges [repulsion] can overcome the binding force of the weak nuclear force. When this happens the atom breaks apart in what we call radiation (typically alpha decay through fission). Adding more neutrons can separate the protons enough to keep the atom stable as neutrons add the weak force but are electrically neutral. This only works up to a certain point, after that the atom becomes unstable in relatively small time frames. This upper stability limit is Lead at atomic number 82. Uranium (92) and Plutonium (94) sit beyond this. Plutonium is very hard to find naturally as it's half life(80.3 million years) is low enough that most if not all of the Plutonium from the creation of the solar system has decayed into lighter elements like lead or uranium. Elements higher then Uranium are often called transuranic elements, and don't exist in nature as any that did would have decayed away by now.
https://en.wikipedia.org/wiki/Transuranium_element
Most of these we have manufactured in particle accelerators and some nuclear reactions and some of them tend to decay in fractions of a second that you need scientific notation to measure. These could be a source of some exotic elements, if you could justify their stability. One possibility way to do this would be to have a very young solar system. However, these may not be "exotic" enough, because even though we don't know much about them, we do know a fair bit.
So you can see the way elements are build and what limits them is well understood. It's hard to reason into being some element we could have "missed" with these magic properties, without some hand waving. Well at least for people that have some grasp of nuclear physics.
Possibly a much better bet is compounds or molecules that are exotic. There is a much wider range here, they are less fixed and you can have all kinds of alloys and things that have special properties (meta materials etc). These would be molecules instead of elements. Which may or may not seem to be a big distinction, but it is. So you could probably get a way with some type of exotic ore that has special properties as long as it's not an "element". This could be from a meteorite strike, formation in space uses different conditions then formation on a planet.
The only elemental possibility I can think of is the so called Island of stability.
https://en.wikipedia.org/wiki/Island_of_stability
Which basically postulates that certain high atomic numbers are "magical" and the resulting heavy element would be stable for day, weeks, years or even longer. I haven't done much research into this area, but as far as I know we haven't found any evidence that this is true. In any case you could have some kind of deposit of this "unobtainium" that loosely conformed to the ideas for this.
I think any kind of exotic substance like this requires some amount of hand waving.
When I write about technology and things that are a bit on the edge of what is realistic, I intentionally leave it a bit vague. Over explaining can be a bigger problem then just leaving it up to the readers imagination. Basically you can say things that are impossible in nature, which no matter how well you reason it is still hand waving, or you can leave it a bit vague and let the reader fill in some of those blanks.
Planet specific resource would likely be the combination of elemental distribution, geologic activity and specific animal or plant life. Gold may exist anywhere in the universe, but what about limestone, coal, fossils or petrified wood? These materials take millions of years to create. Just because we humans cover our buildings with it or burn it for electricity doesn't mean that an alien civilization hasn't found a way to create wormholes with it. (That would be an ironic story: the unobtainium that fueled an intergalactic empire was burned up to make electricity on humble little Earth.)
All the gold on earth came from elsewhere in space. So something similar could have happened on an alien planet, they got bombarded by meteoroids etc,. which had concentrations of something that is incredibly rare on Earth. A gold rich planet would be a pretty good find if gold retains the value it has now.
Most of Earths gold is locked up in the molten core. Possibly an alien planet has it's resources much easier to get at, then having the same volume as Earth but easy to get at would make a huge difference.
I always think of them as isotopes with such a large difference in neutrons that they have different chemical properties.
The fact that these things aren't conceivable under our current understanding of physics is kind of the point. We have no idea how it got there and no idea how to make it. That's why it's rare, and that's why we have to go to that planet to get it. Maybe it was left over from the previous big bang, or from another universe entirely. Maybe Q put it there just to f*ck with us.
So much of the universe's mass is unaccounted for. There's only protons, neutrons and electrons around this neighborhood, but who knows what's really out there?
