  This paper is concerned with the ergodic subspaces of the state spaces of
isolated quantum systems. We prove a new ergodic theorem for closed quantum
systems which shows that the equilibrium state of the system takes the form of
a grand canonical density matrix involving a complete commuting set of
observables including the Hamiltonian. The result obtained, which is derived
for a generic finite-dimensional quantum system, shows that the equilibrium
state arising from unitary evolution is always expressible in the canonical
form, without the consideration of a system-bath decomposition.
