What experiments have been done on Identical Particles?

Question

Are elementary particles really identical, or do they have hidden state? I have learned / always assumed that any two electrons are identical and interchangeable; the same for any other elementary particle. They may have spin, or higher energy, but they don't have the kind of nearly-infinite internal state that, say, two baseballs have.

I am looking for any experiments that have tried to prove, or more likely to disprove, that particles are "identical".

I'll try to make up an example of such an experiment: Take pairs of entangled electrons, and separate those with different spins into two groups. Use a particle accelerator to fire each group into an "equivalent" mass of hydrogen nuclei, and measure if the way they interact with the mass is different in some consistent way.

Maybe this examples is fundamentally flawed -- if the spin should affect the interaction. My intent is some contrived experiment where we try to separate particles into groups in ways that are distinct and reproducible, but the separation itself should not cause a change to any known state of the particles)

Searching this site, I couldn't find exactly the question posed, nor any citation of evidence. I did find the presumption assumed/stated in a few places:

1. "elementary particles ... can be described by only specifying their impulse and another discrete set of quantum numbers" (How can a truly elementary particle change into other particles?)

2. "there's no guarantee that muons aren't composite. But there are many compelling experimental and theoretical reasons suggesting so." (Why are muons considered to be "elementary particles" in the Standard Model?)

3. "an it be that two free electron are identical?" (Is uniqueness a fundamental property of nature?) - the broader question was "closed as unclear"; although the second answer did state "Current theories do assume though that all elementary particles of the same kind are identical"

And from random googling:

4. Identical particles on wikipedia states it as a given, that there "are particles that cannot be distinguished from one another, even in principle".

5. Maybe related to the Pauli exclusion principle, but I don't understand this well enough to see if this directly provides a stance on my question; and I couldn't find any relevant experiments linked from this article.

Answer 1

The Gibbs Paradox might be worth looking up, as regards a theoretical basis for identical particle, and experimentally AFAIK, no experiment has ever observed a process that contravenes the second law of thermodynamics.