Local thermal rectification law

Thermal rectification which is a diode-like behavior of heat flux has been studied over a long time. However, a universal and systematic physical description is still lacking. In this letter, a perturbation theory of thermal rectification is developed, which provides an analytical formula of the thermal rectification ratio. It reveals the linear relationship between the thermal rectification ratio and temperature difference. Furthermore, the size-dependence of the thermal rectification relies on the specific form of the thermal conductivity. In addition, several experimental and numerical observations in previous literatures are well explained. This theory can be applicable to any system in which a differentiable effective thermal conductivity can be derived, and is helpful to unveil general principle for thermal rectification.