The rearrangement of species in the vicinity of coherent interfaces be
tween chemically distinct vacancy-free solid substances is analyzed in
the framework of thermodynamics. Irreversible thermodynamics show tha
t two surface dissipative tensors are required for a consistent descri
ption of slow rearrangement at coherent interfaces, contrary to grease
d interfaces and free boundaries which require only one dissipative su
rface tensor of self-diffusion. The additional tensor (named the tenso
r of in-plane rearrangement) pertains to the interfaces between solid
substances. The governing system of rearrangement postulated is concep
tually the simplest; it is used for establishing the simplest dispersi
on equations revealing the physics of the interface rearrangement proc
esses.