# 4: Statistical Ensembles

- Page ID
- 18567

- 4.2: The Quantum Mechanical Trace
- Thus far our understanding of ergodicity is rooted in the dynamics of classical mechanics. A Hamiltonian flow which is ergodic is one in which time averages can be replaced by phase space averages using the microcanonical ensemble. What happens, though, if our system is quantum mechanical, as all systems ultimately are?

*Thumbnail: A model of noninteracting spin dimers on a lattice. Each red dot represents a classical spin for which \(\sigma_{j}=\pm 1\).*