  We present a numerical approach to construct a non-equilibrium many-body
statistical operator $\hat{\rho}_\mathrm{rel}$ for an adaptive subspace of
relevant quasi-bound electronic states in a semiconductor nanowire-based
field-effect transistor (NWFET). As a constraint for $\hat{\rho}_\mathrm{rel}$,
we assume that the single-particle density matrix $\rho_1$ is a given quantity,
resulting from a non-equilibrium Green's function (NEGF) calculation for the
NWFET for a given set of applied voltages. Two different orthonormal (ON)
eigenbases for $\hat{\rho}_\mathrm{rel}$ are considered: (A) a Slater
determinant basis of natural orbitals (eigenstates of $\rho_1$) and (B) the
eigenbasis of the projected many-body Hamiltonian $\hat{H}_\mathrm{rel}$ within
a relevant Fock subspace of the system. As for the eigenvalues $w_n$ of
$\hat{\rho}_\mathrm{rel}$, we furthermore assume that $w_n$ have a generalized
Boltzmann form, parameterized by effective electrochemical potentials of
natural orbitals and a given temperature. From the determined
$\hat{\rho}_\mathrm{rel}$, in turn, one can calculate expectation values for
any many-body observable within the relevant subspace. As an example, we
analyze the electron density and the covariance of the density-density
correlation function for representative electronic preparations of the NWFET.
