bonvoyage36

4 ms·

1. 1.▲
   by bonvoyage36 1y ago

   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. What you mean can be properly phrased as &quot
2. 2.▲
   by bonvoyage36 1y ago

   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 evolution equations, not solutions.
3. 3.▲
   by bonvoyage36 1y ago

   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 state and a simpler evolution equation for it is made. Often
4. 4.▲
   by bonvoyage36 1y ago

   equations can be time-symmetric, or invariant re time reversal. What you're describing is equations being invariant re time reversal.
5. 5.▲
   by bonvoyage36 1y ago

   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. However, typical initial conditions imply transitions to equi