Ehrenfest's Double-Urn Game
Ehrenfest's Double-Urn Game
Statistical irreversibility as an explanation of the direction of time's arrow has been presented in various ways. The principle of statistical irreversibility postulates that some states that are physically possible will not occur because of extremely low probability [1, 2]. The physicist Paul Ehrenfest (1880–1933) showed this elegantly in a game with one simple rule: there are balls unequally or equally divided between two urns A and B. A ball is chosen at random. If it happens to be in urn A, it moves to urn B, and if it happens to be in urn B, it moves to urn A. The process is repeated, and it is seen that after a while, regardless of the total number of balls and the balls' initial distribution between the urns, the system reaches a dynamic equilibrium around . Also, unless the total initial number of balls in the two urns is very small, or the numbers in each urn are about equal, the original distribution is unlikely to be restored, regardless of how long one waits.
n
n/2