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I really like this concept!

Reminds me a bit of Scott's Ars Longa, Vita Brevis.

  1. Cars in a parking lot: they enter an leave mostly independently. The turnover time for residential parking might be a day or two. For a shopping center it is a few hours.
  2. Bugs in software: they get introduced and then fixed somewhat independently. The turnover time is on the order of weeks to months, maybe days if the project is very active, or even years for very subtle bugs.
  3. Water molecules in a lake: "new" ones flow in, get mixed up with the existing ones, and roughly independently flow out again. The turnover time depends on the influx/outflux and volume. For example Lake Constance has a volume of 48 km³ and average influx of 370 m³/s, making the turnover time about 4 years.
  1. Stable equilibrium: The surface of a pond when I throw something in. I might be interested in the overall water level, which slowly changes over days and weeks. At these timescales the surface is always in equilibrium. (Equilibrates quickly re what I'm interested in)
  2. Bistability: The ruling party in a democracy. Mostly stable over a monthly to yearly timescale. I need to worry about who to vote for once every few years, not every day. (Equilibrates quickly re what I'm interested in)
  3. Dynamic equilibrium: The amount of train delays per day in a city. If I'm in the city right now, I care about the current situation and not that incentives might reduce the amount of delays in the long run. (Equilibrates slowly re what I'm interested in)
  1. The demand for toilet paper. On a short-term timescale there'll be random peaks and troughs (or not so random ones due to people expecting a lockdown). But in the medium-term it'll be constant, because of each person only needing a fairly constant amount of toilet paper. Although in the long-term there'll be changes again due to a growing or shrinking population.
  2. The amount of train delays per day in a city. Some days have more, e.g. because of some big event or a random accident, while other days have fewer. But on average over weeks or months it is roughly constant. 
  3. The amount of groceries in my fridge. I go shopping roughly once a week, so in between the amount steadily goes down and then jumps up again. There might be some irregularities due to eating out or being especially hungry, but over longer periods of time I mostly eat the same amount.

How the equilibrium gets restored in each direction:

  1. If above equilibrium (people buying lots of toilet paper for a while) the demand will be lower afterwards. If below equilibrium they'll run out eventually and the demand will tick up again.
  2. If above equilibrium (a lot of delays) over a longer period of time, people might get upset and the operating company might try to improve scheduling, maintenance, number of trains etc. If below equilibrium, the operators might for example get complacent and stop putting in as much effort.
  3. If above equilibrium (eaten a below average amount from my fridge and have a lot of groceries left at the end of the week), I'll just buy less. If below equilibrium I'll have to buy more when I go shopping, or maybe go more than once per week.

I think my browser tab and social interaction examples on the post on stable equilibria fit in better here. They're much more dynamic than stable.

I really like the chess example. Anything continuous that gets discretized is similar. Like the color of a pixel in a photo, or whether you have crossed the finish line in a race.

  1. A seesaw on a playground. Either side will come back down again if it's perturbed a little (given it's reasonably well oiled etc).

    People sitting on it and literally kicking with their feet is enough to kick it into a different state. Random noise due to wind is not strong enough, except maybe in a heavy storm.
  2. The handle of a window (usually). Pointing in one direction when closed and another when open. It will stay in either position unless explicitly moved (which makes it different from a door handle).

    The activation energy required to kick it depends on whether it's oiled or rusty etc.
  3. The ruling party / coalition in a democracy. (In general multistable, but in the US you might call it bistable). One type of perturbation are attempted coups, which will be squashed when not strong enough.

    Elections are kicks. But only when the elected party is actually different, which might happen when the voters are dissatisfied with the previous one strongly enough, or the election campaign was just better, etc. Another kick would be a successful coup.
  1. The even surface of a pond. If I throw in a stone it'll ripple for a while, but the additional activity will dissipate again.
  2. The number of tabs I have open in my browser. If it's very few I have no problem opening and keeping new ones. If it's too many, titles become hard to read etc. and I feel reluctant to keep open additional ones and tend to close a bunch of them at once.
  3. The amount of social interaction I get. Too little and I feel lonely and reach out to people. Too much and I feel overwhelmed and keep to myself for a while.

In economics (and I’m sure in many other fields - I’m just writing about what I know here), something like this is supposedly done in the “robustness checks” section of a paper.

Machine learning sometimes has ablation studies, where you remove various components of your system and rerun everything. To figure out whether the fancy new layer you added actually contributes to the overall performance.