Sixteen balls, elastic walls, no friction. Collision times are solved exactly, so the table runs backwards as cleanly as it runs forwards — the physics forgets nothing. Everything that gets lost here is lost by you. Two knobs: how wrong your starting knowledge is, and how carefully you are looking.
All three resolutions are measured on the same run, every step. Switch the knob and the whole history redraws: same balls, same collisions, a different answer to “what is the entropy of this table right now”. None of them is wrong. The rate belongs to the dynamics; the amount and the ceiling belong to the question you were able to ask.
Takes the one true table, rounds every position and velocity to that many digits, flips every velocity, and runs it forward again for exactly as long as it has been running. Reversibility is real — it just belongs to whoever can afford the notebook.
A classical demonstration about determinism and limited knowledge. It is NOT quantum mechanics and claims nothing about nature. This page runs the same event-driven engine as the lab, checked against it to the last digit, on the article’s full four-thousand-universe ensemble; the cloud you see is a 300-universe sample of it, drawn so the canvas stays smooth. The measured version, its controls and its limits are in “I Never Understood Entropy” in the Quest for Entropy series.