A thought-provoking piece in Venkatesh Rao's Ribbon Farm by akkartik.
What if it's not stable, though. What if societies are only metastable, which I think is far more likely. Metastability, for the uninitiated, is a situation in which forces can be balanced, but that perturbations in the system tend to grow with time, whereas in a truly stable system, perturbations decay with time. In the classic example, a ball at the bottom of a hill is stable, because if it is knocked a little to the left or right, it will fall back to its original spot. However, a ball at the apex of a hill is still forced balanced, but any bump, and it's never going to spontaneously return whence it came.
Similarly, I think we would have a hard time arguing that our society is actually stable, although the analogy with pure physics might be a bit thin. Perhaps this is one reason that our institutions degrade over time. They need constant nudging back to the top of the hill, so we get layers upon layers of bureaucracy to keep the ball in place. Same thing with, say, support for the poor. Wealth is out of their grasp, so we invent complex institutions to make sure they stay above water. The situation not only son't be, but can't be, fixed organically, because it is energetically unfavorable.
So, eventually, we run out of gas, and the ball rolls to the bottom of the energy well. How fast and how hard it falls depend on how much energy it too to prop it up in the first place. The Soviet Union, for example, only lasted mere decades, because it was a contrivance that required bureaucracy, brutality and relentless spying just to keep the whole thing duct taped together. The United States, on the other hand, has basically developed on its own, although in recent years has required a lot more top down maintenance to keep afloat. I think, however, collapse is not just likely, but inevitable, no matter what the system.