This is a rather general question: assume I have a system that has a certain 'forgetful' property, which means that while I can offset its current state for a moment, it will eventually return to its undisturbed state. An example would be a length of river (say, 100 m) from which I extract a certain amount of water: two days later it would not matter if I had removed the water or not. The system would not show any traces of my previous actions. The opposite case would be a rock, a chunk of which I chisel away. Two days later the gap would still remain; the 'system' would never return to its original state.
What would you call a system that displays such 'forgetfulness'?