Gravitational Thermodynamics

The gravitational N-body problem, for $N>2$, is the oldest unsolved problem in mathematical physics. Some of the most ideal examples that can be found in nature are globular star clusters, with $N\sim {10}^6$. In this overview, I discuss six types of fundamental sources of unpredictability, each of which poses a different challenge to attempts to determine the long-term behavior of these systems, governed by a peculiar type of thermodynamics.