CARBON OSCILLATOR MODEL FIG. S2: Model used in the molecular dynamics simulations. We used this model to determine the temperature profile along the outer tube as a function of time once the thermal gradient is created. The analysis of the movement of the inner tube motion provided the values for the parameters F$_{vdw}$ , | dT/dx | , γ , and α . 13 The model used in the molecular dynamics simulations is represented in Fig. S2. It is formed by a double-walled carbon nanotube with combination (10,10)@(15,15). Outer tube atoms that are fixed during the simulations are represented in blue, thermostated atoms in yellow ( T$_{1}$ ) and red ( T$_{2}$ ). Temperatures T$_{1}$ and T$_{2}$ were imposed at the beginning of the simulations.