Sinai's theorem

Sinai’s theorem concerns the behavior of certain complex systems, specifically those involving random environments and dynamic processes like weather or particle movement. It states that for these systems, long-term averages—such as average weather patterns or particle trajectories—become predictable and follow a stable distribution over time, despite the randomness and chaos initially involved. Essentially, Sinai’s theorem assures that, over a long period, the system's behavior settles into a consistent statistical pattern, allowing us to understand and anticipate its general tendencies even amidst short-term unpredictability.