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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'?

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  • $\begingroup$ A system that only operates on our time scale. We humans are unable to observe the larger world and time scale. If some arrogant home owner decided he wanted to change the flora and fauna of 'his' property, it would only be for a short time. 'His' property will most certainly revert to the original ecosystem. We humans can not make self sustaining ecosystems. Just without our grasp. $\endgroup$ – stormy Mar 1 '18 at 22:13
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How would you call a system that displays such 'forgetfulness'?

In one word, dissipative. In multiple words, a system whose autocorrelation function tends to zero as time tends to infinity.

Note that the autocorrelation function may not exist; this concept implicitly assumes a linear (or approximately linear) system. Consider a river. Adding a small impulse of water upstream (e.g., a not-too-large downburst) results in the river flow increasing briefly but eventually stabilizing to some nominal value. Adding a slightly larger impulse results in a similar but slightly larger response. But adding a huge impulse of water upstream (e.g., a very large and rapid snowmelt) may cause the river to carve itself a new channel. With this huge impulse, the flow at some downstream point will increase initially but then drop to zero and stay that way because the river no longer flows past that point.

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From physics standpoint I would say that such system is stable. For example think of a ball on a surface. If the ball is initially on the top of a hill a push would move the ball into the slope that would only accelerate it further from the original location/state (unstable system). If the ball is instead initially in a pit or local minimum, any push would move the ball to the slope only to turn back towards its original location (stable system).

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Terms that come to mind are self or continuously or automatically:

  • restoring
  • replenishing
  • renewing
  • regenerating
  • repairing
  • healing
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In biology this would be a form of Homeostasis, a tendency to a particular optimum state.

That could apply to your case too I think.

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Here's a couple of terms that describe what you're asking for:

(a guess I'm sort of adding to @Fred's list)

  • Balanced system
  • Stable system
  • Revertible system
  • Reproducible system
  • Regressive system
  • Reconstructive system
  • Reestablishing system
  • Re-creative system
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