Matteo Polettini, Diffusion in nonuniform temperature and its geometric analog,
Phys. Rev. E 87, 032126 (2013), arXiv:1211.6580
“Pebbles in a driveway accumulate on the side. In the driveway they are agitated (hot region). They are left undisturbed on the side (cold region)”, wrote Landauer. In this paper I proposed a theory of the diffusion of particles in a fluid where there exists a gradients of temperature, under the assumption that locally, in a small region of the fluid that is approximately at the same temperature, energy equipartition holds. Remarkably, the theory is equivalent to the theory of a particle diffusing at uniform temperature, but on a curved space. Thus according to this theory a temperature gradient can be seen as a deformation of space.