  The unitary dynamics of isolated quantum systems does not allow a pure state
to thermalize. Because of that, if an isolated quantum system equilibrates, it
will do so to the predictions of the so-called "diagonal ensemble" $\rho_{DE}$.
Building on the intuition provided by Jaynes' maximum entropy principle, in
this paper we present a novel technique to generate progressively better
approximations to $\rho_{DE}$. As an example, we write down a hierarchical set
of ensembles which can be used to describe the equilibrium physics of small
isolated quantum systems, going beyond the "thermal ansatz" of Gibbs ensembles.
