Existence of negative differential thermal conductance in one-dimensional diffusive thermal transport

We show that in a finite one-dimensional (1D) system with diffusive thermal transport described by the Fourier's law, negative differential thermal conductance (NDTC) cannot occur when the temperature at one end is fixed and there are no abrupt junctions. We demonstrate that NDTC in this case requires the presence of junction(s) with temperature-dependent thermal contact resistance (TCR). We derive a necessary and sufficient condition for the existence of NDTC in terms of the properties of the TCR for systems with a single junction. We show that under certain circumstances we even could have infinite (negative or positive) differential thermal conductance in the presence of the TCR. Our predictions provide theoretical basis for constructing NDTC-based devices, such as thermal amplifiers, oscillators, and logic devices.