Is probability of occurrence is the right thing to discuss? Consider that the probability of a Gaussian random variable resolving to 0 is exactly 0. We wouldn't say that it's not possible for that random variable to resolve to 0.

I like this perspective as a matter of science communication. The examples are probably best when you can at least attempt to attach a number to them, to show how much more probable they are than macroscopic entropy decrease. For example, you could probably put a rough number on your lightning example (notwithstanding that people would probably start to get very paranoid and stay inside after the first few thousand strikes, but at least it is something).

I think this answer is spot-on. Consider that given the question "can a human jump over a jumbo jet", most of us would not hesitate to say "no" (either on this site or in normal conversation), but for some reason these time reversal questions get us to bend over backwards to never say "never". If you accept these stupendously unlikely events as physically possible, the term "physically impossible" loses all meaning.

@CarlLeth clouds entrain and detrain and entrain again. Does that violate the law of entropy locally ?

This is a VERY good answer. The first two paragraphs draw your attention to the fact that when you deal with phenomena outside your everyday experience you cannot just continue to use your everyday vocabulary without being really specific about it.

I would agree more with this answer if you argued that something with such a small probability of occurring (that isn't also within a continuous set of events that, when considered together, end up being quite likely, such as hitting a specific point on a dartboard) shouldn't fall within the definition of "possible", rather than arguing that doesn't fall within the definition.

Joined physics.SE just to upvote this. Great intuition priming with the examples!

"William Shakespeare is still alive" - that is a fact, either true or false (clearly false by everything we currently know) quite different from the possibility of an egg re-forming, which is merely a matter of adding up probabilities.

I would so love this answer if OP had asked "is it possible?". Your answer would be great to discuss stuff with vaccine naysayers; with lottery players etc.; or with people trying to bend the (probabilistic) laws of physics to whatever they want to achieve. In all those kinds of discussions, we hear this answer much too seldom. Alas, OP asks "non-zero probability" which clearly means he is actually asking about that "stupendously super-duper unlikely" possibility, which, by all intents and purposes is not zero, so in this particular case this answer is simply wrong.

It might be summarized as "this is not forbidden by quantum mechanics, but it will never happen in the observable universe". The rest is indeed an exercise in communication.

@Polygorial the question body says "is there a non-zero probability" but the question title says "Can XYZ happen?". All you have to do to make this answer relevant again is map "can"/"cannot" to "possible"/"impossible", and I see no reason not to do that.

@MikeBrockington> this example clearly considers this statement not from the "fact" standpoint but the "what everyone believes about it is actually wrong" standpoint. Plus if I wanted to nitpick on the nitpick, I would argue you're quite fast giving predicate quality to a statement that is not even clearly defined (which William Shakespeare? what does "alive" actually mean in physics terms?)

Others rightly point out that OP didn't even mention the words "possible" and "impossible," but even still, I simply disagree with the premise of (most of) this answer. "Possible" may be an awful choice for the situation, but "impossible" is simply factually untrue to the implication of the fluctuation theorem, which OP correctly interpreted and is asking about. It is possible to emphasize how staggeringly unlikely this occurrence is (which this answer does well) without splitting hairs about common use notions of possibility, which is really more opinion-based.

I disagree with the premise here. Possible means possible. If the probability is strictly positive (as it certainly is in this case), then it is possible. There is no other way to interpret that word in my opinion. Even some events whose probability is exactly 0 are possible. I don't even see the need to inject "technically" in there. It's just what "possible" means. I see no two ways about it.

@Arthur This may help you understand OP: is it possible for George Washington to serve a third term as president? Would you argue it's possible for all the atoms of his body spontaneously tunnel back together, congress repeals the 22nd amendment and everyone votes for him? This isn't forbidden by quantum mechanics just like with the egg, right? If you want to "not see two ways about it" you basically can't rule out anything happening in the course of your day-to-day life ever, which is dysfunctional and unrealistic. OP is just saying that's poor communication.

@user1717828 Context matters. A lot. Because with it covers implicit assumptions. If you ask about the egg, the context is physics, and the egg reassembling breaks no physical laws and has positive probability. So it's possible. With poor old George, I have two things to say: 1) Yes, that is possible, and 2) when asking that, people who listen will make assumptions that you're not just asking the physical question, but also the medical and legal questions at the same time. And while physically it's possible, medically it's not. Legally is the least of his hurdles.

When people say "technically it's possible" in these matters, what they often mean is "if we look at it from pure physics, there are ways for it to happen and it's possible". With George that's a reframing / specification of context that's relevant. With the egg, asked on this site, that's already the default assumption.

why does your answer make me want to research the number of lightning storms globally per year, the average number of lightning bolts per lightning storm, and how many people can theoretically be killed by a single lightning bolt, just to figure out if scenario 3 is at all thinkable or would require more lightning storms than usual?

A hypothetical Kardeshev 3 civilization, which uses all matter and energy in an entire galaxy to do physics computations and solve optimization problems, could probably make this happen

In the lightning version, I am not so sure because it is a multiplication of many low-probability, but very possible events. But the comparison is generally okay :-)

I make the argument that it is very important to distinguish between "possible but improbable" and really impossible, because the difference conveys something important about the subject and the conditions that would need to be met for it to happen. For George, the conditions require discussion of constitutional amendments; Whether he people would consider him competent in modern times; Whether any equivalent set of atoms would suffice (Ship of Theseus); Contemplation on the existence of souls;

So, beyond purely the pure physics possibilities, "technically possible" is a lead in to separating the probabilities, it's a starting point not ending. It has a close relative, "currently impossible", since a third term is "impossible under current rules". Dropping the qualifier leads to an implication that it can't become possible in the future. Consider the conditions involved in detecting gravity waves or neutrinos, and the work done to make that possible. Consider also sigma confidence.

And, since the subject of English was mentioned, we have many words available here.. Impossible, conceivable, improbable, possible, plausible, probable, likely, certain, and more. Possible is not the same as plausible. The examples are highly implausible, but impossible is an absolute that in itself contains a burden of proof for claiming such.