how would you do the following?

Cringe. I think I know where you're headed, but I don't think the whole second half is what you intended. Entropy is rather far from luck, and entropy isn't disorder, though it is frequently mis-taught that way. Chaos is much closer to what you seem to be thinking than is entropy. You're talking about making more predictable what is not very predictable, which would be making a chaotic system less chaotic.

Still, I know of no way to do this within Hermetic magic. The closest I've thought of would be Faerie Magic's Story Magic (HoH:MC p.98).

Glamour has been used in canon to cheat size in just such a way.

Oh, so you're playing Mage the Ascencion?

no, to the medieval mind, Entropy is not really a concept, and as such it has no place in Ars Magica. Similarly, 'blasts' of abstract force isn't really a thing in Ars Magica, nor something to be desired.

Absolutely. This concept was defined mid 1800, and was purely linked to a physical phenomenon. No correlation to luck.

Luck on the other hand is "very real", in the sense that Fortuna or Fors Fortuna as divinity of luck and fate exists in the Roman mythology.
Now, the interesting point is that Fortuna is not pure luck, it is also fate and destiny. So it seems that if a mage could integrate Fortunam from the Learned Magician, luck could have its own Form. The way Fortunam is described in Hedge Magic looks likes it is affecting mostly random event, but can be used to grant a bonus for specific activities.

"Chaos" exists in the Greek mythology, but is describded as a shapeless mass, where the first divinity came from.
It is not matching the modern concept of entropy, except for its shapeless status. Chaos is more akin to a primordial ooze where everything originated from. Closer to the vision of Chaos as Moorcock described it in his various cycles, without its destructive urge.
However, if a mage would look at improving Creo (creation of full-fledge human life with soul and everything ?), contacting a Daimon of Chaos could be an interesting lead - and of course would open the whole discussion about Creation of human and soul being the only perview of the Divine - but it would make an interesting - if not theological - Saga.

Canonically, the Glamour Mystery plus experimentation (that might, say, have persuaded a faerie to lend a hand, unbeknownst to the Hermetic magus) has been sufficient.
We do not know if the Glamour Mystery on its own is also sufficient.
We do not know if anything beyond vanilla Hermetic magic is necessary: making a hut larger inside than it is outside might well be covered by the Muto guidelines that change the target into something "highly unnatural".

First, this is experimentation, not any sort of original research. Scipio's scores were not high enough to make such a Lesser Enchanted Device without the bonus from experimentation. The rules for such experimentation are given in the core book. Then note that when effects have had special modifiers due to experimentation, it has been explicitly written with them. See Image of the Lady and Servant of Fire in that same section for examples, though there are other examples in the book as well. This particular effect has no such note at all. Other effects of experimentation have also been listed in the character notes. So we know the only effect on this item's creation from experimentation was a bonus to the lab total. Thus, if you have high enough scores, this can be created without experimentation.

right,the fortunam is more or less waht i had in mind. however curiously the book doesn't mention anything about integrating it. so i assumed, the implication was that the 10 forms can do it themselves?

concerning creatin/destroying ideas. i did not mean it in the strictly mental(i.e brain) sense. for instance a particular medieval silk weaving guild is an "idea" the mandate of heaven in chinese philosophy is an idea,which if attacked,can be withdrawn and can even have a domino effect of physical consequences.or increasing the idea of progressivism might help the democratic party win the next election. and so on

I'm fine with Hermetic Magic not being perfect, not being able to do everything.

Sure. But the results of experimentation can be unpredictable and unreplicable.

This is a fallacy.
We know that in some cases "special" effects have been explicitly attributed to experimentation.
We do not know if that's true in every case.

Thus, one cannot assume that the Glamour Mystery can replicate the feat on its own.
At the same time, one cannot assume that "vanilla" Hermetic magic cannot replicate the feat on its own.
In fact, I suspect that leaving this aspect undefined is a conscious decision of the author/editor, so as to leave all possibilities open - both to troupes who want "fully Hermetic" babayaga huts (which are, after all a staple of myth), and to troupes who want "space warping" out of their games.

I know what you mean from the pure logical standpoint, divorcing it from the context. But let's include the context, specifically what is written about these descriptions.

(underline mine)

You see, I'm not making an assumption based on a few cases. I'm noting that the descriptions are "full." If they are missing relevant R/T/D/base/similar information, they are not full. Thus the descriptions of their creation would not be full descriptions if they lacked notes about abnormalities due to experimentation; changes due to experimentation are considered part of a "full description," as evidenced by specific notes when there are abnormalities. So, according to the explanation in the very book we're referencing, we do know it's true in every case.

for the record, since misconceptions abound, entropy is defined as the heat energy divided by the temperature. So in actuality ignem magic could handle this quite nicely, though it wouldn't be described in those terms.

That would be the 'old', 'classical', or 'macroscopic' definition. But it'll do for any non-microscopic discussion.
However you define it though, the concept does not pre-date 1850, and so is irrelevant in mythic europe.

I hadn't wanted to go into too many technical things about entropy and chaos, but as things are headed there...

Eh, close. First, there isn't just one definition. What you've stated is roughly the macroscopic definition, though you've actually defined the change (usually necessarily infinitesimal as you've written it) in entropy, not the entropy itself. (And I might note for those who don't know, heat is a transfer of energy, not energy something possesses.) There is also a microscopic definition based on the number of microscopic configurations for a macroscopic state.

The best way I've heard to describe it outside of a formal definition I got from a chemistry professor ranting about how problematic it is that so many teachers teach that entropy is disorder. He was hoping teachers would switch to explaining that the second law of thermodynamics describes the tendency for energy to spread out, not the tendency for things to become more disordered.

yes, but the microstates definition is not established under thermodynamic laws (which by definition del with heat exchange) and are in effect nothing more than mental masturbation to try and fit misconceptions regarding entropy into a formal definition. The law of entropy is that entropy- as defined by heat energy divided by temperature- will increase. Since in a closed system energy is neither created nor destroyed this means that temperature will generally go down in order for entropy to go up, thus the concept of the heat death of the universe.
I can call a crowd of comedians standing on the top of a ship as a deck of cards, but that doesn't mean I can use them to play poker.

Since misconceptions are abounding, let me try to fix some, including addressing how some modern science can be used to an extent with ArM5.

The second law of thermodynamics does NOT state that the entropy in a closed system will increase. It states the entropy will not decrease. ∆S≥0 is not the same as ∆S>0.

It's dS=dQ/T or ∆S=integral of dQ/T, not S=Q/T nor S=∆Q/T nor S=E/T. These are VERY different mathematically.

No, just no. That is such a generalization that it's invalid way too often to be an acceptable generalization. Look at radioactive decay, for example. For a more readily doable case, pour lots of 0°C water on some really cold (well below 0°C) ice (water ice) in an insulated container. Afterward you will have 0°C ice water.

The problem here is the misuse of the formula as I noted above. If you only allow heat to flow between the two bodies, you get the system's incremental change in entropy as
∆S = dQ/Tc + (-dQ)/Th = dQ(Th-Tc)/(ThTc),
where Th is the hotter temperature and Tc is colder temperature. So this tells us we have heat flow from hot to cold.

So, sure, entropy is part of thermodynamics, and you can link that to Ignem. However, handling probability with Ignem based on this reasoning requires us to misunderstand what entropy is. Entropy is not randomness. If you want to use modern understanding to go along with luck, you really want to talk about chaos in many situations, not entropy.

Now, with ArM5 based on what we got from the Greeks, some things can be used better. The Greeks theorized atoms. Insert molecules, and things are closer. They also theorized the shape of the atom was related to its macroscopic behavior, and we see this in many ways. The microscope structure of molecules and atoms give rise to macroscopic behaviors. Also, Aristotle's "nature place" could be related to Hamiltonian dynamics, and Hamiltonian dynamics is used in classical mechanics as well as the Hamiltonian operator being fundamentally important in quantum mechanics. "Natural place" could also be connected to things like Pauli exclusion and neutron degeneracy pressure. So there are a lot of ways we could mesh things together for those who desire it. That's probably of more value if someone wants to work ArM5 into a modern setting, though.

The more on-topic bit would be chaos. Rego to reduce the chaos in a system would make it more predictable, essentially controlling luck. That comes back to non-general control of luck, but rather using Rego to control outcomes instead of relying on luck. I suppose you could just nudge with Rego instead of using full control, though.

Actually in my engineering class on thermodynamics it was described that entropy is defined as the heat energy over temperature but since it is impossible to know the actual heat energy of any given system the change in heat energy is used instead since they are, in practical terms, the same.
And yes there are exceptions, but for the most part those can be overcome by enlarging what you consider to be the system- radioactive decay being the exception since that is a non-reversible reaction. My point however was not the accuracy of the conclusion, but rather that the idea of temperature being a net decrease led to the idea of the heat death of the universe, which then began to spin into alternate non-scientific ideas as to what entropy meant, since there can be change in temperature within a single body, if that body is a gas. (PV=nRT), which is how we got work from heat in the first place which necessitated the development/understanding of these laws.
(note: by development I mean the human process of the discovery and codification of how things work, not implying that humans create reality or any such gobbledygook)

Engineers tend (IME) to have a somewhat superficial understanding of Entropy - and of physics in general.
Exceptions exist, obviously.

I think you are reading too much in the word "full". What we have is a full description of the end result of the enchantment/invention process, the actual creation. What we do not necessarily have is a full description of is the process by which it was obtained; we obviously do not know, for example, exactly what bonus the experimentation roll yielded.

Note the same use of circular logic as before. You write: "Thus the descriptions of their creation would not be full descriptions if they lacked notes about abnormalities due to experimentation; changes due to experimentation are considered part of a "full description," as evidenced by specific notes when there are abnormalities." I've underlined the point where the fallacy hides: you are using "when" to mean "in all cases when", while the logically correct reading should be "in some cases when". It's like saying that someone who owns only the ArM5 corebook owns the entire ArM5 line, because since he obviously owns a book when it's part of the line, there cannot be books in the line he does not own.

I am not sure hermetic magic can affect probability
but they can learn the arts of learned magicians who have one art affecting luck

Here is the reasoning:

  1. Spell descriptions include design.
  2. These are full spell descriptions, meaning they lack nothing from a spell description.
  3. Therefore they include all design information, not just some of it.
    Where is the circle, please?

I think you just misread a couple things. I wrote "evidenced," not "proven," for a reason. If my interpretation is correct, based on the number of seasons of experimentation, we should see a certain number of side effects. If we do not see an appropriate number, my interpretation is likely incorrect. Only "some" of Scipio's spells were created using experimentation. Two of them show up with notes. We know there are more, though we don't know which spells. Odds are that roughly 2-3 of the spells should have side effects. So the number of written side effects is consistent with all side effects being listed.

Why did I write "when"? Because notes at other times would not be evidence of it, though we do see notes when Virtues are used, such as Glamour. Did I use it to mean in all cases? No, that's not at all what I wrote. For example, there is a law in my state for protecting emergency personnel, as evidenced by cars pulling over a lane when approaching emergency vehicles. Yes, I used "when," because cars pulling over for other reasons such as to pass another car are irrelevant to the law. However, not all cars pull over as they should; but the statement is still correct, so "when" doesn't mean in all cases in such a statement. Thus "when" used here does not imply what you say it does; that's just your misreading.

"Design" is one of "several factors that describe [a spell] for game use" (ArM5 p.115-116), and items just fire off spells. Lab total is not listed as part of the description. Neither is the number of seasons an individual used to make the item.

Now, results of experimentation and similar are not explicitly necessary as part of the description. But "design" is one of the "factors that describe it for game use." Only the parenthetical note at the end is explicitly required. So if my logic is in error, it's here. Now let's see the consequences of such design notes not being part of the full description...

Note that one of the purposes of the "full description" is so that player's may have their magi develop these effects from scratch. No, I'm not just guessing at that being a purpose; we're told that explicitly. If we don't have the details on how the spell is made, we can't replicate it. Let's continue with that. Many of Scipio's spells were created with experimentation, but far from all. The only ones we specifically know of are the two whose side effects are listed. So any of the others could be. With your interpretation, no one may use any of these except the two with listed side effects as guides to make spells from scratch because we don't know what the experimentation did. And those two only work out of you get exactly the same experimentation oddities. Concientia experimented some, but we don't know how much. So we can't use any of her spells. And she doesn't even list using experimentation in the years' summary. So if it's not listed there and not necessarily listed in spells, that could be true of the other magi's spells as well. So we can't use any spells in the entire book for a player to follow to make them from scratch. So your contention is that in writing "full descriptions" with the intention of allowing players to use those "full descriptions" to develop such spells from scratch, the authors failed.

It gets worse. Many example magi in different books have spells not published elsewhere without notes about not using experimentation. Same problem: we can't use them to make new spells.

It gets even worse. Some spells in the core book come from non-Hermetic sources or special research, and that can stop magi from making variants of them. See Aegis of the Hearth and probably Whispering Winds for examples. Most spells have no such notes. So now we can't use most spells in the core book to make them from scratch. For instance, is Lungs of the Fish a special oddity from something non-Hermetic or from research, or is that just the way MuAq(Au) should work? Do we let magi invent Pilum of Fire or variants of it on their own? Should it not be +10 damage, put perhaps the shape was a side effect from experimentation instead of being "purely cosmetic"? What about Arc of Fiery Ribbons and its shape(s)?

My contention is that the authors of MoH did not fail at one of the explicit purposes of writing "full descriptions," or, in other words, that what is explicitly written in the book is correct about the very same book. In order for this to be the case, design modifications due to experimentation (and Virtues, etc.) must be part of the "full description."

No, you can't do that. In Mythic Europe, the physical world gains it reality with its connection to Platonic Forms. What you are describing as ideas are in Mythic Europe Platonic Forms. You can't change a Platonic Form, because its essential nature is unchanging.