  Thermo-osmotic flows, generated by applying a thermal gradient along a
liquid-solid interface, could be harnessed to convert waste heat into
electricity. While this phenomenon has been known for almost a century, there
is a crucial need to gain a better understanding of the molecular origins of
thermo-osmosis. In this paper, we start by detailing the multiple contributions
to thermo-osmosis. We then showcase three approaches to compute the
thermo-osmotic coefficient using molecular dynamics; a first method based on
the computation of the interfacial enthalpy excess and Derjaguin's theoretical
framework, a second approach based on the computation of the interfacial
entropy excess using the so-called dry-surface method, and a novel
non-equilibrium method to compute the thermo-osmotic coefficient in a periodic
channel. We show that the three methods align with each other, in particular
for smooth surfaces. In addition, for a polarized graphene-water interface, we
observe large variations of thermo-osmotic responses, and multiple changes in
flow direction with increasing surface charge. Overall, this study showcases
the versatility of osmotic flows and calls for experimental investigation of
thermo-osmotic behavior in the vicinity of charged surfaces.
