Analytical expression of negative differential thermal resistance in a macroscopic heterojunction

Heat flux ($J$) generally increases with temperature difference in a material. A differential coefficient of $J$ against temperature ($T$) is called differential thermal conductance ($k$), and an inverse of $k$ is differential thermal resistance ($r$). Although $k$ and $r$ are generally positive, they can be negative in a macroscopic heterojunction with positive $T$-dependent interfacial thermal resistance (ITR). The negative differential thermal resistance (NDTR) effect is an important effect that can realize thermal transistor, thermal memory, and thermal logic gate. In this paper, we examine analytical expressions of $J$, $k$, $r$, and other related quantities as a function of parameters related to thermal conductivity ($\kappa$) and ITR in a macroscopic heterojunction to precisely describe the NDTR effect.