Relative stability in nonuniform temperature

Landauer has suggested that the relative stability of a particle diffusing in a bistable potential is affected by an intervening hot layer. We derive this effect both from thermodynamics and from the diffusion equation. For this purpose the proper form of the diffusion equation in a nonuniform medium is established for the case of a Brownian particle. If the diffusion takes place in a ring, the hot layer creates a steady current.