Eigenstate thermalisation hypothesis

Let $A$ be a few-body observable, and let $|E_k\rangle$ be an eigenvector of the Hamiltonian of a large interacting many-body system with energy $E_k$. Eigenstate thermalisation hypothesis. The expectation value of $A$ in this eigenvector equals the thermal average of $A$ at the mean energy $E_k$:

$$\langle E_k|A|E_k\rangle = \langle A\rangle_{\mathrm{thermal},E_k}.$$

The ETH is a central proposed explanation for why closed interacting quantum systems can exhibit thermal behaviour, asserting that individual energy eigenstates reproduce thermal expectation values for few-body observables. The source states the hypothesis but gives no resolution status.