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by ndriscoll 925 days ago
Sure but the point is in a closed system, thermodynamic fluctuations alone are going to take eons to make your house fall down. What will actually get it is that the system is not fully closed, and eventually something from outside the system will give it the activation energy needed to escape the well it's in (e.g. a windstorm causing a tree to fall on it). But it's useful and practical to think of that larger system as decomposing into a product of pretty much independent systems (until it isn't).

The point is wells exist and are common in day-to-day life, including ones that are deep enough that things don't randomly thermodynamically pop out of them. If something is sitting on your desk when you go to bed, you can be pretty certain it'll be there in the morning too. The scale of the well is orders of magnitude larger than the thermal fluctuations, even if eventually a fluctuation could excite your computer monitor to suddenly vaporize. The atoms in your body and all matter will eventually decay to nothing too, but it's not useful to think about that.

And even if it's metastable, as long as the system stays inside the well, the potential is locally quadratic. So you see oscillations around the equilibrium in the meantime.

1 comments

Almost all of reality isnt day-to-day life --- indeed what that describes is, in many ways, exactly the sort of illusions of stability that admit cute mathematical analysis.

You're weighting parts of reality by their relevance to a us at a particular place and time -- without such prejudice you find that very little admits of this sort of cute mathematical description.

And that which does is now pretty exhausted as far as research goes. Describing beds is not a pressing theoretical quesiton

Describing organic systems, say is -- chaotic organic development across trillions of cells. There are no SHOs there

Really? What about the Krebs cycle?
There is no first order taylor series expansion of the krebs cycle -- indeed not.

As soon as you have three of anythign physics, as applied math, breaks down