  We show how to evaluate mobility profiles, characterizing the transport of
confined fluids under a perturbation, from equilibrium molecular simulations.
The correlation functions derived with the Green-Kubo formalism are difficult
to sample accurately and we consider two complementary strategies: improving
the spacial sampling thanks to a new estimator of the local fluxes involving
the forces acting on the particles in addition to their positions and
velocities, and improving temporal sampling thanks to the Einstein-Helfand
approach instead of the Green-Kubo one. We illustrate this method on the case
of a binary mixture confined between parallel walls, under a pressure or
chemical potential gradient. All equilibrium methods are compared to standard
non-equilibrium molecular dynamics (NEMD) and provide the correct mobility
profiles. We recover quantitatively fluid viscosity and diffusio-osmostic
mobility in the bulk part of the pore. Interestingly, the matrix of mobility
profiles for local fluxes is not symmetric, unlike the Onsager matrix for the
total fluxes. Even the most computationally efficient equilibrium method
(Einstein-Helfand combined with the force-based estimator) remains less
efficient than NEMD to determine a single mobility profile. However, the
equilibrium approach provides all responses to all perturbations
simultaneously, whereas NEMD requires the simulation of several types of
perturbations to determine the various responses, each with different
magnitudes to check the validity of the linear regime. While NEMD seems more
competitive for the present example, the balance should be different for more
complex systems, in particular for electrolyte solutions for the responses to
pressure, salt concentration and electric potential gradients.
