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

TL;DR

This paper demonstrates that negative differential thermal conductance in 1D diffusive systems requires junctions with temperature-dependent contact resistance, providing a theoretical foundation for designing thermal devices like amplifiers and oscillators.

Contribution

It establishes the necessary and sufficient conditions for NDTC in 1D systems with junctions, highlighting the role of temperature-dependent contact resistance.

Findings

NDTC cannot occur in fixed-temperature boundary systems without junctions.

NDTC requires junctions with temperature-dependent thermal contact resistance.

Infinite differential thermal conductance can occur under certain TCR conditions.

Abstract

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. 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.