  The diagonal ensemble is the infinite time average of a quantum state
following unitary dynamics. In analogy to the time average of a classical phase
space dynamics, it is intimately related to the ergodic properties of the
quantum system giving information on the spreading of the initial state in the
eigenstates of the Hamiltonian. In this work we apply a concept from quantum
information, known as total correlations, to the diagonal ensemble. Forming an
upper-bound on the multipartite entanglement, it quantifies the combination of
both classical and quantum correlations in a mixed state. We generalize the
total correlations of the diagonal ensemble to more general $\alpha$-Renyi
entropies and focus on the the cases $\alpha=1$ and $\alpha=2$ with further
numerical extensions in mind. Here we show that the total correlations of the
diagonal ensemble is a generic indicator of ergodicity breaking, displaying a
sub-extensive behaviour when the system is ergodic. We demonstrate this by
investigating its scaling in a range of spin chain models focusing not only on
the cases of integrability breaking but also emphasize its role in
understanding the transition from an ergodic to a many body localized phase in
systems with disorder or quasi-periodicity.
