Joule expansion of a pure many-body state

TL;DR

This paper derives the quantum mechanical basis for Joule expansion in an isolated pure many-body gas, showing how thermodynamic properties emerge without factorization of the Hilbert space, including for Bose gases below condensation temperature.

Contribution

It provides a quantum mechanical derivation of Joule expansion for pure states, extending thermodynamics to non-factorizable many-body systems.

Findings

Density characterized by chemical potential and temperature

Expansion described for pure states without Hilbert space factorization

Special case analysis for Bose gases below condensation temperature

Abstract

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 gas many-body Hilbert space cannot be factorised into Hilbert spaces corresponding to interesting and ignored degrees of freedom. Moreover, the expansion of the gas into the entire accessible volume is obtained for pure states. Still, the number particle density is characterised by a chemical potential and a temperature. We discuss the special case of a boson gas below the Bose condensation temperature.