Lynden-Bell theory

Lynden-Bell theory explains how systems with many particles, like star clusters or galaxy groups, reach a stable state after evolving for a long time. Instead of continuously changing, these systems settle into a kind of equilibrium that resembles a maximum entropy distribution, considering the constraints like energy and number of particles. The theory predicts how particles distribute themselves in space and velocity once the system "mixes" thoroughly, helping us understand large-scale cosmic structures without assuming each particle's exact history. It's a way to statistically describe complex gravitational systems after they have evolved.