  When applied to binary solutions, thermal gradients lead to the generation of
concentration-gradients and thus to inhomogeneous systems. While being known
for more than 150 years, the molecular origins for this phenomenon are still
debated, and there is no consensus on the underlying physical models or
theories that could explain the amplitude of the concentration gradient in
response to a given temperature gradients. Notably, there have been some
attempts to relate this non-equilibrium, steady-state manifestation, to
equilibrium properties of these solutions, for example, to the temperature
dependence of the self-diffusion coefficient or to the solvation free-energies
of each of their components. Here, we use molecular dynamics simulations on
dilute solutions containing molecular size solutes, both in a thermophoretic
setting as well as under equilibrium conditions, to test the validity of such
models. We show that these approaches are inadequate and lead to completely
uncorrelated estimates as compared to those based on the out-of-equilibrium
measurements. Crucially, they fail to explain the strong mass-dependence (to
which thermodynamics or single particle diffusion are insensitive) observed in
the simulations and measured in the experiments. However, our results suggest
an interesting correlation between the amplitude of the short-time molecular
motion and that of the concentration-gradient that would deserve future
investigations.
