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

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.