Fig. S3 presents the temperature profile of the outer tube for the system (10,10)@(15,15) for different times after a thermal gradient of 7 K/nm is imposed between the two extremities of the outer tube. As we can see an approximately linear variation of the temperature with x is attained after about 50 ps, the period P of p ( t ) should be larger than 100 ps in order to keep the CNT oscillator operating in the constant thermal gradient regime. As mentioned in the main text the behavior of the thermophoretically driven CNT oscilla- tor depends upon both the inner tube length and the thermal gradient. In order to evaluate this dependence, we identified the cases where there is an oscillation (regular or chaotic) of the inner tube. In such cases the motion is limited within the outer tube. On the other hand, for some set of parameters, the inner tube was strongly accelerated and ejected off the outer tube. The evolution of the inner tube position was obtained by numerical integration 14 TEMPERATURE PROFILE DEPENDENCE UPON TUBE LENGTHS AND THERMAL GRADIENTS FIG. S3: Temperature profile of the outer tube (15,15) for the model of Fig. S2 at different times of the simulation. The temperature was obtained from the kinetic energy of atoms averaged over equally spaced regions of 1 nm. 0 20 40 60 80 100 x (nm) 200 400 600 800 1000 1200 Temperature (K) 5 ps 50 ps 200 ps