The First Law of Complexodynamics

Scott Aaronson asks why physical systems become more “interesting” before settling into disorder, even though entropy only increases. Using a coffee cup example (separate → swirling patterns → fully mixed), he proposes “complextropy”: a resource-bounded version of Kolmogorov sophistication measuring the shortest efficient program that can generate states resembling the observed one. Efficiency constraints are crucial; without them, the measure is trivial. He conjectures complextropy follows a small-large-small pattern over time and suggests testing it experimentally with compression-based approximations on simulations.

Sources: paper