The force of attraction between two solids with different temperatures

The methods of fluctuation electrodynamics and the molecular cohesive force theory have been used to obtain an expression for the attractive force density between two absorbing media varying in temperature and separated by a nonabsorbing plane-parallel layer. The spectral density of the attractive force was calculated as the stress tensor projection on the exterior normal to the solid surface. The mean-square characteristics of the fluctuation field of these media were sought using the generalized Kirchhoff's law and the Green function of the related regular problem. A variety of solutions have been obtained depending on a temperature relationship of the interacting solid media. It is shown that for solids of the same temperature the obtained expression yields a formula describing the force of attraction in equilibrium.