Four-terminal thermal conductance of mesoscopic dielectric systems

A four-terminal thermal conductance formula for a mesoscopic dielectric system with arbitrary central scattering region is derived. Similar to four-terminal electric conductance, the four-terminal thermal conductance also has a set of Onsager relations. In the temperature T-->0 limit, in contrast to the two-terminal thermal conductance which is a monotonic function of T and tends to zero, the four-terminal thermal conductance is nonmonotonic and tends to infinity. We also find that temperatures of the two terminals without thermal flux become very close to each other at low temperatures. Rather different behaviors are found for systems satisfying fractional exclusion statistics.