Reiter's Theorem

Reiter's Theorem states that the smallest set of rules (called a "Gibbs measure") describing a system with many components (like particles or spins) can be characterized by local conditions. Specifically, understanding the behavior in small parts and how they connect allows us to describe the entire system's complexity. This theorem is fundamental in statistical mechanics and probability theory because it links local interactions to the overall global behavior, ensuring that the system's large-scale distribution is consistent with known rules governing each small region.