  Thermal gradients lead to macroscopic fluid motion if a confining surface is
present along the gradient. This fundamental nonequilibrium effect, known as
thermo-osmosis, is held responsible for particle thermophoresis in colloidal
suspensions. A unified approach for thermo-osmosis in liquids and in gases is
still lacking. Linear Response Theory is generalised to inhomogeneous
systems,leading to an exact microscopic theory for the thermo-osmotic flow
showing that the effect originates from two independent physical mechanisms,
playing different roles in the gas and liquid phases, reducing to known
expressions in the appropriate limits.
