We present a dynamic mean field theory (DMFT) and nonequilibrium dual control volume grand canonical molecular dynamics (GCMD) simulation study of steady-state fluid transport in slit-shaped mesopores under an applied chemical potential gradient. The main focus is on states where the bulk conditions on one side of the pore would lead to a capillary condensed state in the pore at equilibrium while those on the other side would lead to a vapor state in the pore. This choice of conditions is motivated by certain separation applications in which condensable vapors permeate through mesoporous membranes. Under these circumstances, we have found partially filled states with a liquid-like state at the high chemical potential end of the pore and a vapor-like state at the low chemical potential end. This phenomenon is accompanied by hysteresis. The existence of partially filled states has been hypothesized in previous work but the present paper reveals them as an emergent feature of the systems. We find that predictions of DMFT are in good qualitative agreement with the overall GCMD results. However, the GCMD results demonstrate that the transport is faster through the partially filled pore than through the unfilled pore, a feature not captured by DMFT.