Joule expansion of a pure many-body state.

We derive the Joule expansion of an isolated perfect gas from the principles of quantum mechanics. Contrary to most studies of irreversible processes which consider composite systems, the interesting and ignored degrees of freedom are here described by operators acting in the same many-body Hilbert space. Moreover, the expansion of the gas into the entire accessible volume is obtained for pure states. Still, the number particle density is characterized by a chemical potential and a temperature. We discuss the special case of a boson gas below the Bose condensation temperature.