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

## TL;DR

This study explores the full temperature and size dependence of thermal conductance in a 1D nonlinear lattice, revealing a universal fat-tailed distribution and asymptotic power-law behavior.

## Contribution

It introduces a comprehensive analysis of thermal conductance dependence on temperature and size, demonstrating a universal q-Gaussian scaling law.

## Key findings

- Thermal conductance follows a fat-tailed q-Gaussian distribution with respect to temperature and size.
- The asymptotic behavior at high temperatures is characterized by a power-law decay with exponent approximately 3.64.
- Data collapse indicates a universal scaling law across different system sizes and temperatures.

## Abstract

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 $TN^{1/3}$ with $q \simeq 1.55$. Consequently, its $T \to\infty$ asymptotic behavior is given by $T^{-\alpha}$ with $\alpha=2/(q-1) \simeq 3.64$.