[kgwgk]

> I thought the 2nd law of thermodynamics was saying that with incomplete knowledge, the probability distribution of possible states becomes more and more spread out as time goes on. It's almost a limit to how you can make predictions or simulations of physics when the initial state of the system is not fully known. Equivalently, it's a banal statement about chaos in the sense of chaos theory.

I'm not sure I understand what do you mean by "as time goes on". Classical thermodynamical entropy is defined for a system in equilibrium and it doesn't change with time. It changes when you do things to the system.

[ogogmad]

I don't think statistical mechanics entropy is limited in this way. I think the (incorrect? oversimplified?) definition given in the article is only valid under the conditions you've given. But I'm not sure.

[kgwgk]

Then it maybe depends on what you meant by "the 2nd law of thermodynamics".