We carry our study of internal energy, and the correlation between macroscopic system behaviour and microscopic behaviour, into the realm of statistics. Any particular molecule in a gas, or vibrational mode in a system of radiation, or atom in a crystal, is subject to random fluctuations in its energy state. But when a vast number of particles are coupled together to form a system, the system as a whole exhibits quite definite and predetermined thermodynamic behaviour. We have to find techniques which can bridge the conceptual gap between microscopic uncertainty and macroscopic determinism.