All the molecules start on the left. Remove the partition and they spread until both halves hold about the same number. Nobody aimed them there; it is simply that far more arrangements look even than look one-sided.
The gas expands into vacuum, so it pushes nothing and does no work. No heat crosses either, so the internal energy is unchanged and the temperature never moves. That is what separates free expansion from the adiabatic expansion on the process page, where the gas cools because it works on the piston.
The record is S ／ Nk ＝ −(p ln p ＋ q ln q), taken from the fraction p on the left. It starts at 0, climbs to ln2 ＝ 0.693 when the split is even, and then only jitters. It never walks back down to 0. Putting the partition back takes your hand, and that asymmetry is the second law.
The panel names at the top right open and close each panel. Drag a panel by its header to move it: panels snap to each other and to the screen edge, and a panel resting on an edge drops the rounded corner on that side. Double-click a panel title to switch between floating panels and a single fixed panel at the top right. Pick a row in the condition panel and its value appears in the child panel beside it, which follows the parent as it moves.