We consider the possibility of using a quasi-equilibrium approximation for multi-scale simulations of the transport of a closely fitting nanometer-size solid sphere through a fluid-filled cylindrical nanochannel (Phys. Rev. Lett. 89, 244501, 2002). To this end, by means of molecular dynamics simulations, we compute the force acting on the sphere slowly approaching the wall and then receding to its original position at the center of the tube. We find that the effective free-energy of the system exhibits substantial hysteresis as a function of the radial position of the particle. This clearly indicates that the multiscale description of the system should include an additional order parameter or reaction coordinate. For example, the number of fluid molecules inside the gap, which shows hysteretic behavior similar to that of the effective free-energy, may perhaps be used as such a parameter.