This post explores why physical systems’ “complexity” rises, peaks, then falls over time, unlike entropy, which always increases. Using Kolmogorov complexity and the notion of “sophistication,” the author proposes a formal way to capture this pattern, introducing the idea of “complextropy” — a complexity measure that’s low in both highly ordered and fully random states but peaks during intermediate, evolving phases. He suggests using computational resource bounds to make the measure meaningful and proposes both theoretical and empirical (e.g., using file compression) approaches to test this idea, acknowledging it as an open problem.