Thermal conductance of the coupled-rotator chain: Influence of temperature and size

Thermal conductance of a homogeneous 1D nonlinear lattice system with neareast neighbor interactions has recently been computationally studied in detail by Li et al [Eur. Phys. J. B {\bf 88}, 182 (2015)], where its power-law dependence on temperature $T$ for high temperatures is shown. Here, we address its entire temperature dependence, in addition to its dependence on the size $N$ of the system. We obtain a neat data collapse for arbitrary temperatures and system sizes, and numerically show that the thermal conductance curve is quite satisfactorily described by a fat-tailed $q$-Gaussian dependence on $T{N}^{1\mathrm{/}3}$ with $q\simeq 1.55$. Consequently, its $T\to \mathrm{\infty }$ asymptotic behavior is given by $T^{-\alpha }$ with $\alpha =2\mathrm{/}(q-1)\simeq 3.64$.