  We extend Expanded Wang-Landau (EWL) simulations beyond classical systems and
develop the EWL method for systems modeled with a tight-binding Hamiltonian. We
then apply the method to determine the partition function and thus all
thermodynamic properties, including the Gibbs free energy and entropy, of the
fluid phases of Si. We compare the results from quantum many-body (QMB) tight
binding models, which explicitly calculate the overlap between the atomic
orbitals of neighboring atoms, to those obtained with classical many-body force
fields (CMB), which allow to recover the tetrahedral organization in condensed
phases of Si through e.g. a repulsive 3-body term that favors the ideal
tetrahedral angle. Along the vapor-liquid coexistence, between 3000K and 6000K,
the densities for the two coexisting phases are found to vary significantly (by
$5$ orders of magnitude for the vapor and by up to 25% for the liquid) and to
provide a stringent test of the models. Transitions from vapor to liquid are
predicted to occur for chemical potentials that are $10-15$% higher for CMB
models than for QMB models, and a ranking of the force fields is provided by
comparing the predictions for the vapor pressure to the experimental data. QMB
models also reveal the formation of a gap in the electronic density of states
of the coexisting liquid at high temperatures. Subjecting Si to a nanoscopic
confinement has a dramatic effect on the phase diagram, with e.g. at 6000K a
decrease in liquid densities by about 50% for both CMB and QMB models and an
increase in vapor densities between 90% (CMB) and 170% (QMB). The results
presented here provide a full picture of the impact of the strategy (CMB or
QMB) chosen to model many-body effects on the thermodynamic properties of the
fluid phases of Si.
