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) ∈ (-∞,+∞) 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) ≠ 0, NDTR can 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.