Understanding thermo-osmosis in nanoscale channels and pores is essential for both theoretical advances of thermally induced mass flow and a wide range of emerging industrial applications. We present a new mechanistic understanding and quantification of thermo-osmosis at nanometric/sub-nanometric length scales and link the outcomes with the non-equilibrium thermodynamics of the phenomenon. The work is focused on thermo-osmosis of water in quartz slit nanochannels, which is analysed by molecular dynamics (MD) simulations of mechano-caloric and thermo-osmotic systems. We investigate the applicability of Onsager reciprocal relation, irreversible thermodynamics, and continuum fluid mechanics at the nanoscale. Further, we analyse the effects of channel size on the thermo-osmosis coefficient, and show, for the first time, that these arise from specific liquid structures dictated by the channel size. The mechanical conditions of the interfacial water under different temperatures are quantified using a continuum approach (pressure tensor distribution) and a discrete approach (body force per molecule) to elucidate the underlying mechanism of thermo-osmosis. The results show that the fluid molecules located in the boundary layers adjacent to the solid surfaces experience a driving force which generates the thermo-osmotic flow. While the findings provide a fundamental understanding of thermo-osmosis, the methods developed provide a route for analysis of the entire class of coupled heat and mass transport phenomena in nanoscale structures.