Absence of thermal rectification in asymmetric harmonic chains with self-consistent reservoirs

An exact analysis using the Langevin equation approach proves that an asymmetric-inhomogeneous harmonic chain with self-consistent inner reservoirs does not rectify heat, while it may show diffusive heat transport properties. Thus, we argue that the onset of a formal Fourier's law in an asymmetric system does not guarantee an asymmetric heat flow.