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That just looks like a conserved property. I know those are linked to symmetries, but they're not identical.

Is this something like the physical operation to invert it doesn't exist, even though it's logically possible? The "pants" example, and maybe the superposition example, makes it sound like they're uninvertible for entropy reasons, which seems interesting if it's not an illusion.

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Right, they're not identical, but they're generally paired up so neatly via Noether's theorem that they're treated as the same thing.

In seems like physicists are finding more general conserved quantities associated with more general spaces of physical operations such that not every action is reversible, but there are still conserved quantities associated to the underlying systems, AKA symmetries.

I don't have any solid physical intuition as to what makes an operation irreversible in this context, though, whether it's related to entropy or not.

Interesting. Thanks!

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