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.
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