We know from Quantum complexity theory, that the vast majority of states in Hilbert space for physically relevant Hamiltonians cannot be accessed except in exponentially long time (see related questions here, and here). Thus, for a solid with $\sim10^{23}$ constituents, most of Hilbert space is irrelevant.
One of the building blocks of statistical mechanics of quantum systems is to assume a Gibbs distribution and ergodicity of the eigenstates. One expects the quantum system a non-zero temperature to be in some Gibbs mixed state of all eigenstates weighted by the Gibbs factor.
However, following the aforementioned result of quantum complexity theory, I would assume that for a generic Hamiltonian that some eigenstates are physically inaccessible in polynomial time. How does one account for those (presumably) inaccessible states in quantum statistical mechanics? If they are unaccounted for, how should one understand those eigenstates and ergodicity in that context?
