One is now interested in studying the time evolution of the system. If a set formula_28 eventually comes to fill all of formula_2 over a long period of time (that is, if formula_30 approaches all of formula_2 for large formula_32), the system is said to be ergodic. If every set formula_14 behaves in this way, the system is a conservative system, placed in contrast to a dissipative system, where some subsets formula_14 wander away, never to be returned to. An example would be water running downhill -- once it's run down, it will never come back up again. The lake that forms at the bottom of this river can, however, become well-mixed. The ergodic decomposition theorem states that every ergodic system can be split into two parts: the conservative part, and the dissipative part.