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It's not a good phrasing to express the point, because "solution is invariant under operation O" has an established meaning, that the solution does no change after the operation. W…

I know what you meant; I've just tried to point out an error in your sentence which pops up sometimes, which may have mislead others. It's all about the time reversal invariance of…

In derivations of the Navier Stokes equations from reversible particle models, the former get their irreversibility from some approximation, e.g. a transition to a less detailed st…

equations can be time-symmetric, or invariant re time reversal. What you're describing is equations being invariant re time reversal.

Strictly speaking, naturally on its own, it doesn't. Detailed equations remain reversible. Even for very big N, typical isolated classical mechanical systems are reversible. Howeve…