  Thermal diffusion has been studied for over 150 years. Despite of the long
history and the increasing importance of the phenomenon, the physics of thermal
diffusion remains poorly understood. In this paper Ludwig's thermal diffusion
is explained using Einstein's random walk. The only new structure added is the
spatial heterogeneity of the random walk to reflect the temperature gradient of
thermal diffusion. Hence, the walk length and the walk speed are location
dependent functions in this paper. Then, a mathematical understanding of such a
random walk gives the foundation of the thermal diffusion as clearly as the
original homogeneous case of Einstein.
