Stephen Wolfram - Computational Foundations for the Second Law of Thermodynamics

So how does this relate to the Second Law? It’s what makes it possible for a system like rule 30 to operate according to a simple underlying rule, yet to intrinsically generate what seems like random behavior. If we could do all the necessary computationally irreducible work then we could in principle “see through” to the simple rules underneath. But the key point (emphasized by our Physics Project) is that observers like us are computationally bounded in our capabilities. And this means that we’re not able to “see through the computational irreducibility”—with the result that the behavior we see “looks random to us”.

And in thermodynamics that “random-looking” behavior is what we associate with heat. And the Second Law assertion that energy associated with systematic mechanical work tends to “degrade into heat” then corresponds to the fact that when there’s computational irreducibility the behavior that’s generated is something we can’t readily “computationally see through”—so that it appears random to us.