Shaking a container is a good example I think, assuming the glass is convex.
Shaking has to be continuous, the particles move quickly and erratically, but they trace continuous paths.
Shaking has to be continuous, the particles move quickly and erratically, but they trace continuous paths.
In an ideal system with points instead of particles, shaking would be continuous.
Think of the 1D variant. If you shuffle a deck of cards, but require that to be ‘continuous’, few shuffles remain (I think only the identity mapping and ‘flipping the deck upside down’). I doubt anybody would restricting the possible permutations that much stil call shuffling.