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Scaling analysis of negative differential thermal resistance

Negative differential thermal resistance (NDTR) can be generated for any one-dimensional heat flow with a temperature-dependent thermal conductivity. In a system-independent scaling analysis, the general condition for the occurrence of NDTR is found to be an inequality with three scaling exponents: $n_{1}n_{2}<-(1+n_{3})$, where $n_{1}\in(-\infty,+\infty)$ describes a particular way of varying the temperature difference, and $n_{2}$ and $n_{3}$ describe, respectively, the dependence of the thermal conductivity on an average temperature and on the temperature difference. For cases with a temperature-dependent thermal conductivity, i.e. $n_{2}\neq0$, NDTR can \emph{always} be generated with a suitable choice of $n_{1}$ such that this inequality is satisfied. The results explain the illusory absence of a NDTR regime in certain lattices and predict new ways of generating NDTR, where such predictions have been verified numerically. The analysis will provide insights for a designing of thermal devices, and for a manipulation of heat flow in experimental systems, such as nanotubes.